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.

Measurement

Systems of Measurement

Measurement around the Globe

Country or Region | System of Measurement | Examples of Units Used |
---|---|---|

Used | Equivalent |
---|---|

Physical 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 |

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

Fig. 1.12 High in accuracy and precision |
Fig. 1.13 High in precision but low in accuracy |
Fig. 1.14 Low in accuracy and precision |

Example:

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 |

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

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 |

Significant Figures

Mass (g) | |
---|---|

Isay | 198.5 |

Kiko | 199 |

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

Significant Figures

1. 43.9820 __________ | 4. 6.0009 __________ |

2. 57.000 __________ | 5. 956 780 __________ |

3. 0.012 __________ | 6. 0.0203 __________ |

• 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

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.

• 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.

Operations 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

Scientific Notation

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

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

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

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.

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

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?

Mass, Volume, Density, and Temperature

Mass

Volume

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

The formula is:

V = Vf – Vi

Density

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 |

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}`

Cross multiply V with D.

m = DV D = 2 g/mL V= 30 mL

Temperature

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?

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

K = 40 + 273.15

K = 313.15 K (final answer)

How Dense Is It?

Object | Mass | Volume | Density |
---|---|---|---|

Eraser | |||

25-centavo coin | |||

Piece of chalk | |||

Marble | |||

Science textbook |

Conversion of Units

Info Overload

Hottest Places

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?

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.

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

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.

1 kg = 1 000 g

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

1 min = 60 s

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