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A.   Identify the word being defined by arranging the jumbled letters. Write the correct word on the blank.

1.    T N R S E E E U A M M – It is the process of comparing an unknown quantity with a standard.

_____________________________________

2.    O E L M – It is a unit used to measure the amount of chemical substance.

_____________________________________

3.    G H L T E N – It is the distance between two points.

_____________________________________

4.    C AC U Y C R A– It refers to the nearness of the measurement to the true value.

_____________________________________

5.    I O P E R S N I C – It refers to the closeness or consistency of measurements.

_____________________________________

 

B.    Use the given clue to solve each cryptogram in which each number represents a letter. Write the number corresponding to each letter of the alphabet. Letter I is given as a headstart

 

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

24

 

1.    These are digits used to tell accuracy in a measurement.

 

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2.    It is a quantity with a fixed numerical value.

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3.    These are zeroes in between nonzero digits.

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4.    These are zeroes found before a nonzero digit.

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Measurement

Measurement is the comparison of an unknown quantity with that of a known quantity. The known quantities are standards that scientists agreed upon, while the unknown quantities are those that you measure. A standard determines the extent a unit of measurement can quantify a certain characteristic. For instance, it tells you how long an inch is or how heavy a kilogram is. Measuring devices are calibrated using standards.

Measurement is evidently important in your daily activities. It is also essential to your study of science. In particular, it will help you in classifying, characterizing, and analyzing matter. Matter has quantitative properties, which are characteristics that can be measured and are usually obtained in experiments. Without measurement, your understanding of matter will be quite different.

 

Systems of Measurement

People in various places around the world have their own standards that comprise a system of measurement. A system of measurement gives you a list of measurable characteristics and the units that you can use to measure them. The units are based on standards that people in that particular place had approved.

There are two prevailing systems of measurement in the world: the English and the metric systems. The English system is used primarily in the United Kingdom. Also known as the Imperial system, the English system has standards that were originally based on body dimensions. An inch was based on the width of a thumb, while a foot was based on the length of the king’s foot. Throughout the years, the English system had been modified several times before it became the version people know it today. Meanwhile, the metric system, which originated in France, is a decimal system based on the unit meter. A meter was originally defined as one-ten millionth of the distance of a line from the equator to the north pole running through Paris. Its definition had also been modified several times until it reached its present definition.

The use of different systems of measurement by scientists posed a problem in the scientific community, especially when presenting quantitative data. To address this concern, scientists convened and developed a system of measurement called the International System of Units in 1960, which is also called SI units based on its French translation, Systeme Internationale d’ Unites. This system is based on seven basic units which measure seven basic properties of substances. The basic units of SI are based on standards kept in the Bureau of Weights and Measures at Sevres, France.

 

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Measurement around the Globe

Research on other systems of measurement aside from the metric and the English systems. Ask also your elders about the different units of measurement that Filipinos use other than the English, metric, or SI units. Use the tables below to present your findings.

 

Systems of Measurement in Other Countries

Country or Region System of Measurement Examples of Units Used

 

 

 

 

 

 

 

 

Philippine System of Measurement

Used Equivalent

 

 

 

 

 

 

 

Physical Quantities

Physical quantities are properties that are clearly defined, can be measured by instruments, and have proper units. They are classified as fundamental and derived quantities. Fundamental quantities are the basic properties of substances. They do not depend on any other physical quantity.

The seven basic SI units are all fundamental quantities. Table 1.7 lists the seven fundamental quantities.

 

Table 1.7 Fundamental Quantities

 

Property/Physical Quantity Definition SI Unit Standard
Length The distance between two points meter (m) Distance traveled by light in a vacuum in {1} over {299 792 458} second
Mass Amount of material in an object kilogram (kg) Equal to the mass of the platinum-iridium international prototype of the kilogram
time An exact duration  of an event second (s) Radiation of cesium-133 atom
Amount of substance Quantity of chemical substance mole (mol) Amount of substance containing the Avogadro’s number, 6.022 × 1023
Temperature The quantity that indicates the hotness or coldness of a substance kelvin (K) Absolute temperature which is equal to temperature in Celsius degree plus 273
Electric current Flow of electric charge ampere (A) 6.241 × 1018 electrons going at a given point per second
Luminous intensity Amount of light emitted in a particular direction candela (cd) Monochromatic radiation of frequency 540 × 1012 hertz

 

 

Derived quantities are other physical quantities derived from the combinations of the seven basic quantities. Area and volume, for example, are derived from length. Their units of measurement are square meter (m2) and cubic meter (m3), respectively. Density is a property derived from mass and length (since volume is derived from length). Its unit is kilogram per cubic meter (kg/m3). Table 1.8 shows the SI base units for some derived quantities.

 

Table 1.8 Examples of Derived Quantities

Physical Quantity SI Base Unit Symbol
Area square meter m2
Volume cubic meter m3
Density kilogram per cubic meter kg/m3
Speed meter per second m/s
Force newton N
Energy joule J
Power watt W
Pressure pascal Pa
Quantity of electricity coulomb C

 

Uncertainty of Measurement

When measuring, errors may occur due to human factors or defects in measuring tools. Thus, a certain degree of uncertainty is allowed in measurement. If this is so, are scientists just wasting their time measuring since they cannot have exact measurements after all? All experimental data have this certain level of error. However, the error may be so numerically small that it is deemed insignificant. Scientists are after an accepted nearness to the exact value, which can already give them a clear picture of what they are measuring.

As a student of science, you are going to do many measurements. Hence, you should remember that measurements must be accurate and precise. Accuracy is the nearness of a measurement to the true value. This refers to your ability to get a measurement that is as close as possible to the correct value. Precision is the closeness of several measurements of the same property for a given substance at a certain condition. This reflects your ability to reproduce the same result or measurement given the same property of the substance at the same condition. Examine the illustrations below.

 

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Fig. 1.12 High in accuracy and precision

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Fig. 1.13 High in precision but low in accuracy

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Fig. 1.14 Low in accuracy and precision

 

Using the illustrations above as guide, create an illustration that shows high in accuracy but low in precision. As a science student, what should you always aim for? Why?

Can you now distinguish between accuracy and precision? Study the example below.

Example:

A glass tube is about 4 inches long. It was passed around to several groups of students. Each group was asked to measure the length of the tube in centimeters (cm). Each group has five members, and each member independently measured the tube and recorded his or her result. A report from the glass factory where the tube was manufactured certifies the tube to be 10.160 cm. Find out which group of students has the most precise and most accurate measurement.

 

Group Student 1 (cm) Student 2 (cm) Student 3 (cm) Student 4 (cm) Student 5 (cm)
A 10.1 10.4 9.6 9.9 10.8
B 10.13 10.22 10.20 10.01 10.15
C 12.14 12.17 12.15 12.14 12.18
D 10.05 10.82 8.01 11.5 10.77
E 10 11 10 10 10

 

The average length of the tube for each group is as follows: A – 10.16 cm, B – 10.14 cm, C – 12.15 cm, D – 10.23 cm, and E – 10.2 cm. Comparing each average length to the reported length of the tube, which is 10.16 cm, you can see that group A has the most accurate results. But is group A’s measurement precise? The values obtained by the students in group A differ significantly. Thus, their result is accurate but not precise. Group C has the most precise measurements. Get the difference between the highest value (12.18 cm) and the lowest value (12.14 cm). The difference is 0.04 cm. Group C’s measurements therefore are precise but not accurate. Group B’s measurements are both accurate and precise because there is a very small difference in the measurements compared to the true value. Group D’s and E’s measurements have low accuracy and low precision.

Accuracy and precision can be used to evaluate sets of data. They can be used as factors that will influence the credibility of data. Accuracy of the results shows whether or not the average of all trials in an experiment is equal to the true value. It means that the measurements are correct. However, precise results can be all close to each other but far from the true value. This could signify a systematic error because of the calibration of the measuring instrument.

A numerical value that represents the nearness of a measurement to the true value is called percent error. It reflects the percentage of the possible error in the measurement with 0% having no error, and thus, is the true value. Getting a 100% error means that no amount of correctness can be applied to the measurement. To get the percent error, use the formula:

 

percent error = {true value - experimental value} over {experimental value} x 100%

 

In application, the average measurement is used as the value.

 

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Coin Measurements

Objective:  Determine the percent error of the mass and the diameter of a 5-peso coin and a 10-peso coin.

Materials:   ruler, triple beam balance or any available balance, one 5-peso coin (minted 1995), one 10-peso coin (minted 2000)

Procedure:

1.    Using the available balance, get the mass of the 5-peso coin. Record it in Data Chart 1 below. Make three trials.

2.    Using a ruler, get the diameter of the 5-peso coin. Record it in Data Chart 2. Make three trials.

3.    Repeat steps 1 and 2 for the 10-peso coin.

4.    Compute the average mass and diameter of each type of coin.

 

Data Chart 1

Coin Trial Average (g) Percent Error
1 (g) 2 (g) 3 (g)
P5
P10

Data Chart 2

Coin Trial Average (cm) Percent Error
1 (cm) 2 (cm) 3 (cm)
P5
P10

 

5.    Using the average value as the experimental value, compute the percent error of the mass and the diameter of each coin. The true values of the coins according to the measurements of Bangko Sentral ng Pilipinas are:

Coin Diameter (mm) Mass
P5 27.0 7.7
P10 26.5 8.7

 

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Significant Figures

Recall that all measurements have a level of uncertainty. Because of this, it is important to take note of the significant figures that are involved in your numerical data. Significant figures are numbers or digits in a given measurement that are reliable. They can be used to determine the precision and accuracy of your results. However, this is not the case all the time.

Consider the following example:

The label of a baby powder indicates that it contains 200 g. Isay and Kiko would like to find out if the label is true. Isay used a triple beam balance, while Kiko used a weighing scale commonly used in the market. They got the following results:

 

 

Mass (g)
Isay 198.5
Kiko 199

 

Isay’s and Kiko’s measurements have different number of significant figures. Using a triple beam balance, Isay found the mass with four significant figures. Using a common weighing scale, Kiko found the mass with three significant figures. Which instrument is more accurate?

Consider another example below:

 

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Measured with a tape measure, how long is the pencil? You can say that it is 5.5 cm long.  But 0.5 cm is just your guess or estimate because the smallest unit you can read using the calibration on the tape measure is 1 cm.  Hence, 5.5 cm only has two significant figures.

 

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Now measure the same pencil with a tape measure with a different calibration. The length of the pencil now reads 5.55 cm. Using the tape measure, you can measure 5.5 cm directly, while 0.05 cm is an estimate because the smallest unit on the tape measure is 1 mm. The length of the pencil (5.55 cm) has three significant figures.

In measuring different objects, the number of significant figures is always considered. The greater the number of significant figures a measuring instrument can read, the more reliable the result would be. When you measure an object using any measuring instrument, all observed measurements include one estimated number. The number you can read directly from the measuring instrument and the estimated number are significant numbers.

The rules in counting the number of significant figures are as follows:

1.    All nonzero digits are significant.

2.    Zeroes can be significant or insignificant depending on their position in the number:

a.    Zeroes located after a nonzero digit are called trailing zeroes. They are not significant if they are located before the decimal point. Trailing zeroes at the right of the decimal point are significant.

Examples:

•    500 has only 1 significant digit

•    5.00 has 3 significant digits

b.    Captive zeroes are zeroes in between nonzero digits. They are always significant.

Examples:

•    505 has 3 significant digits

•    5.05 has 3 significant digits

c.    Leading zeroes are those found before a nonzero digit. They are not significant.

Examples:

•    0.05 has 1 significant digit

•    0.0055 has 2 significant digits

 

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Significant Figures

Count the number of significant figures in each number.

1.   43.9820   __________ 4.   6.0009    __________
2.   57.000     __________ 5.   956 780  __________
3.   0.012       __________ 6.   0.0203    __________

 

Significant figures are used as basis for rounding off. In science, particularly in chemistry, you need to round off all measurements you obtain to the required number of significant digits for convenient handling and presentation of data.

Recall the rules in rounding off numbers:

•      Look at the digit to the right of the rounding digit. If the digit is less than 5, retain the rounding digit; if the digit is 5 or more, add 1 to the rounding digit.

•      For whole numbers, change all the digits to the right of the rounding digit to zero; for decimals, drop all the digits to the right of the rounding digit.

 

Calculations Using Significant Figures

When you are using measurements, you also consider significant figures in your calculations. Here are some rules in doing calculations with significant figures.

1.    Constants used in your calculations do not influence the number of significant figures in your answer. Examples of constants are pi (π), standard pressure, Avogadro’s number, and so on.

2.    In multiplication or division, the answer should have the same number of significant figures as the number (factor, dividend, or divisor) with the lowest number of significant figures.

Examples:

•      123.00 × 114 × 10 = 100 000

The actual product is 140 220.00, but it is rounded off to the nearest hundred thousand because the lowest number of significant figures among the factors is 1.

•     {0.5} over {0.40} = 1

The actual quotient is 1.25, but since 0.5 is the factor with the lowest number of significant figures, then the answer should have only 1 significant figure.

3.    In addition and subtraction, the answer should have the same uncertainty as the number with the largest uncertainty. In other words, the answer should have the same number of decimal places as the number with the least number of decimal places.

Examples:

•      12.1 + 3.59 + 4.202 = 19.9

The actual sum is 19.892, but since 12.1 has the largest uncertainty, the sum is rounded off to

the nearest tenths.

•      45.78 – 23.100 – 12.4967 = 10.18

The actual difference is 10.1833, but it is rounded off to the nearest hundredths because 45.78

has the largest uncertainty.

4.    Pure numbers or exact numbers do not affect the accuracy of your results. They are numbers that have no units.  You may think of pure numbers as numbers with an infinite number of significant figures.

Example:

Three pencils have the following lengths:  10.50 cm, 10.35 cm, and 10.55 cm. What is the average length of the pencil?

•      Get the sum of the lengths.

10.50 cm + 10.35 cm + 10.55 cm = 31.40 cm

•      Divide the sum by 3.

{31.40 cm} over {3} = 10.46666667

The length of the pencil should have 4 significant figures even if you are dividing the sum by a single digit. Thus, the average length of the pencil is 10.47 cm.

 

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Operations Involving Significant Figures

Solve the following items to practice calculations involving significant figures.

1.     {36.31} over {1.3}

2.    1 238.698 – 368.5

3.    63.38 + 9.35 + 3.698

4.    10.11 + 3.5 + 9.230

5.    136.83 – 3.697

6.    113.01 × 5.78

 

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Scientific Notation

Measurements can be very small or very large. In chemistry, Avogadro’s number is used in many computations. Avogadro’s number is equivalent to 602 200 000 000 000 000 000 000.  Expressing very small or very large numbers this way is rather inconvenient. Fortunately, they can be expressed in scientific notation. The original number is called ordinary notation or standard notation.

A number in scientific notation is expressed as A × 10b

where

•      A is the coefficient, which is a number that is at least 1 but less than 10.

•      b is an exponent, which is an integer representing the number of places that the decimal point is moved to make the coefficient fall between 1 and 10.  A negative exponent indicates a number less than zero, while a positive exponent indicates a number greater than zero.

•     10 is the base.  The base is always written as 10 in scientific notation.

 

Writing Numbers in Scientific Notation

To write a large number such as 40 800 000 000 000 in scientific notation, follow these steps:

1.    Move the decimal point to get a number that is at least 1 but less than 10. Drop the numbers that  are not significant.

4.08

2.    Multiply the number by 10.

4.08 × 10

3.    Raise 10 to the number equal to the number of places you moved the decimal point. If the number is greater than 1, the exponent is positive.

4.08 × 1013

To write a small number such as 0.000 009 67 in scientific notation, follow these steps:

1.    Move the decimal point to get a number that is at least 1 but less than 10.

9.67

2.    Multiply the number by 10.

9.67 × 10

3.    Raise 10 to the number equal to the number of places you moved the decimal point.  If the number is greater than 0 but less than 1, the exponent is negative.

9.67 × 10–6

 

Calculations Involving Scientific Notation

Here are some rules when doing calculations involving scientific notation:

 

Addition and Subtraction

Example:  Subtract 2 × 10–7 from 3 × 10–6.

1.    Find the number whose exponent is the smallest. Note that negative numbers are smaller than positive numbers. The farther to the left the integer is from zero on the number line, the smaller it is. In the example, the smaller exponent is –7.

2.    If the exponents of the numbers are not the same, make them the same. Move the decimal point of the coefficient of the number with the smaller exponent to the left, and add one to the exponent of that number, until the two exponents are equal.

2 × 10–7 = 0.2 × 10–6

3.    Add or subtract the coefficients of the two numbers, then copy the base and the exponent.

(3 × 10–6) – (0.2 × 10–6) = (3 – 0.2) × 10–6 = 2.8 × 10–6

4.    Round off the final answer following the rules on significant figures. Since both addends from the given example are whole numbers, the final answer must also be a whole number.

3 × 10–6 – 0.2 × 10–6 = 2.8 × 10–6 = 3 × 10–6

5.    If the sum or difference is not in standard scientific notation, that is, the coefficient is between 1 and 10, simply move the decimal point. If you move the decimal point to the right, subtract 1 from the exponent. If you move the decimal point to the left, add 1 to the exponent.

Examples:

a.    10.83 × 105 is not in standard scientific notation. To convert it to standard scientific notation, move the decimal point one place to the left. Thus, you add 1 to the exponent, which gives 1.083 × 106.

b.    0.0088 × 105 is not in standard scientific notation. To convert it to standard scientific notation, move the decimal point three places to the right. Thus, subtract 3 from the exponent, which gives 8.8 × 102.

 

Multiplication

Example: Multiply 3.3 × 108 and 5.2 × 103.

1.    Multiply the coefficients.

3.3 × 5.2 = 17.16

2.    Multiply the bases (10) by adding their exponents.

17.16 × 10 (8 + 3) = 17.16 × 1011

3.    Write in standard scientific notation.

1.716 × 1012

4.    Round off the final answer following the rules on significant figures. Both factors have one decimal place; therefore, the final product is 1.7 × 1012.

 

Division

Example:  Divide 6.87 × 1025 by 7.87 × 102.

1.    Divide the coefficients.

6.87 ÷ 7.87 = 0.872935197

2.   Divide the bases by subtracting their exponents.

0.872935197 × 10 (25 – 2) = 0.872935197 × 1023

3.    Write in standard scientific notation. Round off the final answer following the rules on significant figures.

0.872935197 × 1023 = 8.73 × 1022

 

 

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Scientific Notation

Answer the following questions.  Express numerical values in scientific notation.

1.    The speed of light is 299 792 458 m/s.  What is the speed of light in scientific notation? Round this off to the nearest hundredths.

2.    The electrical charge of an electron is 0.0000000000000000001602177 coulombs. Express this in scientific notation and round this off to the nearest hundredths.

3.    The mass of an electron is 0.0000000000000000000000000000009109 kg. If an element contains 10 electrons, what is the mass of its electrons?

4.    The mass of a proton is 0.0000000000000000000000000016726 kg. If an element contains 20 electrons and 20 protons, what is the sum of the masses of its electrons and protons?

 

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Mass, Volume, Density, and Temperature

In your study of science, you will learn about matter and its quantitative properties. Some of these properties are mass, volume, density, and temperature.

 

Mass

Mass is the amount of matter in an object. Different types of balances such as the triple beam balance, platform balance, digital top loading balance, and analytical balance can be used to measure mass. The SI unit for mass is kilogram (kg). However, other units such as gram (g) and milligram (mg) are also commonly used.

 

Volume

Volume is the amount of space matter occupies. In the laboratory, the graduated cylinder is used in measuring the volume of liquids and small irregular solids. In using a graduated cylinder, remember to look at the lower meniscus when getting the volume of a colorless liquid and at the upper meniscus if you have a colored liquid.

Volume is a derived quantity; thus, it can be obtained using calculations. To get the volume of a regular solid, measure its dimensions such as width, height, and length. For spherical objects, measure the diameter or radius. Here are some of the formulas used in getting the volume of regular solids:

Cube: V = s3, where s is the length of a side

Rectangular prism: V = L × W × H, where L is the length, W is the width, and H is the height

Sphere = {4} over {3} πr3, where r is the radius

To get the volume of small irregular solids, use the displacement method. This is done by placing a known volume of liquid in the graduated cylinder. This is the initial volume (Vi). Then drop the object carefully into the graduated cylinder. The volume will rise to the final volume (Vf). The volume of the object will be the difference between the two measurements.

The formula is:

V = Vf – Vi

 

Volume is commonly expressed in cubic meters (m3) when using SI. However, some people also use liter (L), milliliter (mL), and cubic centimeter (cm3 or cc).

 

Density

Density is the amount of matter per unit space. It can be simplified as mass (m) per unit volume (V). Thus, its formula is D = {m} over {V} . Density is a derived property, and so it has derived units such as kg/m3 for SI. Some people also make us of g/mL, g/cc, mg/L, mg/cc, and so on.

Density is a unique property of matter, that is, it varies with the kind of substance.

 

Table 1.9 Density of Some Common Substances

 

Material Density (g/mL) Material Density (g/mL)
Cork 0.25 Ice 0.92
Water 1.000 Iron 7.80
Gasoline 0.70 Silver 10.50
Kerosene 0.80 Tin 7.30

 

Density is the reason behind the appearance of layers in a mixture of liquids. It also influences the floating or sinking of a solid when placed in a liquid. When you mix two liquids with different densities, the liquid with the lower density will form a top layer. On the other hand, if the solid placed in a liquid is denser, it will sink; otherwise, it will float.

Mass, volume, and density will be very useful in calculations. Look at the following problems.

1.    Calculate the volume of a stone using the displacement method. The initial volume of the water in the graduated cylinder is 20 mL. When the stone was dropped in the cylinder, the water level rose to 25 mL.

Formula:       V = Vf – Vi

where            Vf = 25 mL          and           Vi = 20 mL

Calculation:  V =25 mL – 20 mL

V = 5 mL (volume of stone)

2.    Calculate the density of the stone in number 1 if its mass is 20 g.

Formula:       D = {m} over {V}

where            m = 20 g          and          V = 5 mL

Calculation:  D = {20 g} over {5 mL}

D =  4 g/mL  (final answer)

3.    What is the mass of an unknown substance that has a density of 2 g/mL and a volume of 30 mL?

Formula:   D = {m} over {V}

 

Derive the equation for the formula for mass.

Cross multiply V with D.

   m = DV    D = 2 g/mL   V= 30 mL

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Temperature

Temperature tells how hot or cold a substance is. It is a quantitative property of matter. Some other properties of matter depend on temperature. The thermometer is the instrument used in measuring temperature.

The Kelvin (K) is the SI unit for temperature. The zero point is considered the lowest possible temperature of anything in the universe that is why the Kelvin scale is called the absolute temperature scale. The Kelvin scale, which is named after William Thomson (also known as Lord Kelvin), has the designated 0 K. In the centigrade scale, it is equivalent to –273.15°C, and in the Fahrenheit scale, it is –459.67°F. Scientists have tried cooling substances near 0 K, but they have yet to achieve it. However, they have successfully cooled substances below 1 K artificially.

Aside from Kelvin, another unit of temperature commonly used in chemistry is Celsius. Laboratory thermometers are usually expressed in Celsius. The Celsius scale is named after Anders Celsius, a Swedish scientist. The freezing point of water is 0°C while the boiling point is 100°C. The relationship between the Celsius scale and the Kelvin scale is K = °C + 273.15. Thus, the freezing point of water is 273.15 K and the boiling point is 373.15 K.

The Fahrenheit scale is named after Gabriel Daniel Fahrenheit. It assigns 32°F as the freezing point of water and 212°F as the boiling point. It is related to the Rankine (R) scale, which was named after a Scottish physicist and engineer, William Rankine. It uses the formula R =°F + 459.67.

The Fahrenheit and Celsius scales are related using the formulas:

 

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Study the following sample problems regarding temperature scales:

1.    The temperature of water is 40°C. What is its temperature in Fahrenheit?

Formula:             °F = °C × 1.8 + 32

Calculation:        °F = 40 × 1.8 + 32

°F = 104°F (final answer)

2.    Thetemperature of tap water that is exposed to sunlight is 104°F. What is this temperature in Kelvin?

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Calculation:  104°F = 40°C (From number 1)

 K = 40 + 273.15

 K = 313.15 K (final answer)

 

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How Dense Is It?

Work in groups of five. Measure the different quantitative properties required for each material. Use measuring tools available in your laboratory. Show your calculations, if any.

Object Mass Volume Density
Eraser
25-centavo coin
Piece of chalk
Marble
Science textbook

 

Conversion of Units

In analyzing measured data, you may encounter different units used for a specific property of the same substance. For example, kilogram and gram may have been used for mass. Centimeters and meters may have been used to measure length. It is necessary to use units consistently, especially when there are calculations involved.

To convert units, dimensional analysis may be used. This method requires the use of conversion factors. A conversion factor relates two units used for the same quantitative property. For gram and kilogram, the conversion factor is 1 kg = 1 000 g. This is the equivalence that can be used to convert grams to kilograms, and vice versa.

Here are some conversion factors that you may use:

Time

1 year (yr) = 12 months (mo)

1 day = 24 hours (h)

1 mo = 4 weeks (wk)

1 h = 60 minutes (min)

1 wk = 7 days

1 min = 60 seconds (s)

 

Mass

1 kilogram (kg) = 1 000 grams (g)

1 g = 1 000 milligrams (mg)

1 kg = 2.2 pounds (lb)

1 ton = 1 016 kg

 

 

Info Overload

 

Hottest Places

The temperature that we have is comparably lower than the hottest spots on Earth. The highest recorded surface temperature was around 70.7°C. It occurred in 2005 at Lut Desert in Iran. Before that, a temperature of 66°C was recorded at El Azizia, Libya in 1922. Other very hot deserts on Earth are found in Mali, Tunisia, Israel, and the Death Valley in California. Extreme heat can cause heat stroke and dehydration.

 

Length

1 mile (mi) = 1.609 kilometers (km)

1 inch (in) = 2.54 centimeters (cm)

1 meter (m) = 1.09 yards (yd)   

1 foot (ft) = 12 in       

1 yard = 3 feet (ft)

1 km = 1 000 m

1 m = 100 cm

1 cm = 10 millimeters (mm)

 

Volume

1 liter (L) = 1 000 milliliters (mL)

1 mL = 1 cubic centimeter (cc or cm3)

 

Study the following conversion problems:

1.    Lisa bought 12 kg of rice from the supermarket. What is the mass of rice in g?

Conversion factor:  1 kg = 1 000 g

The conversion factor will be expressed as a fraction with the denominator having the same unit as the measurement to be converted. This will allow cancellation of units.

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2.    The length of the glass tube is 200 cm. What is the length of the glass tube in inches?

Conversion factor:   1 in = 2.54 cm

 

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3.    Nico weighs 55 lb. What is Nico’s mass in grams?

There is no conversion factor for lb to g. However, there is a conversion factor from lb to kg, and then from kg to g.

Conversion factors:    1 kg = 2.2 lb

1 kg = 1 000 g

Calculation: This conversion involves two steps.

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4.    Jeffrey’s travel time from Manila to Cabanatuan is 4 h. How much time in seconds did it take Jeffrey to reach Cabanatuan?

Conversion factors:    1 h = 60 min

1 min = 60 s

Calculation: The conversion can be done in a single equation with both conversion factors incorporated in the solution.
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