# KSU Distance And Logitude Measurements Worksheet

Measurement, Numbers & Dimensional AnalysisEXERCISE 1

Part 1: Measurements

Observe the markings on a ruler and use the ruler to measure the following items.

Item

Length (m)

Estimated Digit

Number of

Significant Figures

Width of little

fingernail

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enter text.

Click or tap here to

enter text.

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enter text.

Length of a shoe

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enter text.

Click or tap here to

enter text.

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enter text.

Your height

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enter text.

Click or tap here to

enter text.

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enter text.

Part 2: Scientific Notation

1. Using a computer or other resource, determine the mass of earth in kg. Express this

number with and without scientific notation.

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2. An important number used in chemistry is Avogadro’s Number which is used to describe

the number of molecules in a mole of substance (we will discuss Moles in another unit of

this course). Look up this number and express it with and without scientific notation.

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3. Solve the following math problems using scientific notation:

1. 4.9 × 102 + 7.9 × 103

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Measurement, Numbers & Dimensional Analysis

2. 4.801 × 103 − 2.2 × 107

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3. (9 × 10−1 ) × (3 × 1010 )

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4. (3.5 × 10−6 ) ÷ (5 × 10−2 )

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Part 3: Significant Figures

1. For the following numbers below, state the number of significant figures:

1. 0.000420

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2. 6.02 × 1023

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3. 0.00230

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Measurement, Numbers & Dimensional Analysis

2. Round each of the following to two significant figures. Express your answer in scientific

notation.

1. 63.288

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2. 555.1

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3. 0.0000749

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3. Solve the following math problems and write their answers with the correct number of

significant figures.

1. 1.23 + 45.6

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2. 8.3 − 5

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3. 3.4 × 2.32

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4. 78.5 + 0.0021 + 0.0099

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Measurement, Numbers & Dimensional Analysis

5. (2.31 × 103 ) ÷ (3.1 × 102 )

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6. 1.23 × 3.456

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Part 4: Length

Length is defined as the measurement of something from end to end. In the SI system it is

expressed in meters. The meter is the length of the path traveled by light in a vacuum during a

time interval of 1/299792458 of a second.

Use your textbook or the internet to determine the following:

1 in = __________ cm

1 mile = __________ ft

1 km = __________ miles

1 furlong = __________ meters

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1. Using a ruler to measure the length of an 8 2 × 11 sheet of printer paper. Take a photo of

you measuring the paper. Find the relationship between centimeters and inches, and

Measurement, Numbers & Dimensional Analysis

compare to the conversion above.

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2. Measure the width, in inches, of your desk or kitchen table using the tape-measure. Take

a photo of you measuring the table or desk. Record this measurement in inches and

convert it to meters.

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3. Measure the width of a pencil or pen in centimeters and convert it to miles. Take a photo

of you measuring the pencil. Record your answer in scientific notation.

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4. Convert your height in inches to millimeters.

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5. When driving to the store, determine how long your journey is in miles. Convert this

measurement to kilometers and then furlongs.

Measurement, Numbers & Dimensional Analysis

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Part 5: Mass

Mass is the property which reflects the quantity of matter within a sample. The SI unit for

mass is the kilogram. The kilogram equal to the mass of the international prototype of the

kilogram. Additionally, mass can be measured in ounces. There are several standards for the

ounce (see table below). You can see how confusing this would be when selling goods by

this unit of measure.

Ounce Variant

Avoirdupois ounce

Apothecaries’ or troy ounce

Maria Theresa ounce

Spanish ounce

Dutch metric ounce

Chinese metric ounce

Metric ounces

Equivalent in Grams

28.3495231

31.1034768

28.0668000

28.7500000

100.0000000

50.0000000

25.0000000

In addition, the common unit of weight is the Pound. Weight is a measure of force not mass,

but we many times use the pound as a measure of mass. Hence, many times the abbreviation

for pounds when referring to mass is lbm, and lbf when referring to force or weight. Use your

textbook or the internet to determine the following:

1 kg = __________ g

1 kg = __________ lbm

1 slug = __________ lbf

1. The mass in pounds of a gallon of water is 8.34 lbs. Convert this measurement to

kilograms.

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Part 6: Time

Measurement, Numbers & Dimensional Analysis

Time is defined as the measured or measurable period during which an action, process, or

condition exists or continues. It is measured in seconds in the SI system in which the second is

the duration of 9192631770 periods of radiation corresponding to a transition between ground

state levels of cesium 133.

1. How many seconds does it take the earth to make one orbit around the sun?

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2. How many seconds does it take the earth to make one rotation?

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3. How many nanoseconds are in 1 megasecond?

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4. One light year is the distance that light travels in exactly one year. if the speed of light is

6.7 × 108 mph, convert light-years to (a) miles and (b) meters.

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Part 7: Temperature

Temperature is the degree or amount of heat present in a substance. The SI unit for temperature

1

is the kelvin, which is the fraction 273.15 of the temperature of the triple point of water.

Absolute, or thermodynamic, temperature is conventionally measured in kelvins (Celsius-scaled

increments) and in the Rankine scale (Fahrenheit-scaled increments) with increasing rarity.

Absolute temperature measurement is uniquely determined by a multiplicative constant which

𝑇

specifies the size of the “degree”, so the ratios of two absolute temperatures, 𝑇2 , are the same

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in all scales.

Measurement, Numbers & Dimensional Analysis

1. What equation can be used to convert between Celsius and Kelvin?

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2. What equation can be used to convert between Celsius and Fahrenheit?

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3. Use a thermometer to determine your actual body temperature in Fahrenheit. Convert this

temperature to Celsius.

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Part 8: Amounts

The SI derived units are so named because they are obtained from the seven SI base units.

Examples include area (m2), volume (m3), pressure (n/m2), and density (kg/m3).

Volume

Volume is the quantity of three-dimensional space occupied by a liquid, solid, or gas. The

confusing unit of measure known as an ounce.

Use your textbook or the internet to determine the following:

1000 mL = __________ L

1 gallon = __________ L

1 cm3 = __________ mL

1. Using an empty gallon milk jug and a measuring cup you use for cooking, determine how

many cups of water are needed to fill 1 gallon. Take a photo showing how you

accomplished this.

Measurement, Numbers & Dimensional Analysis

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2. Using a tape measure or ruler, measure the radius and height of a cylinder. Take a photo

showing how you accomplished this. Determine the volume in cm3 using the equation

𝑉 = 𝜋𝑟 2 ℎ.

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