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# Conversion Factors Help

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## Conversion Factors

Conversion factors make use of the relationship between two units or quantities expressed in fractional form. The factor-label method (also known as dimensional analysis ) changes one unit to another by using conversion factors.

Conversion factors are helpful when you want to compare two measurements that aren’t in the same units. If given a measurement in meters and the map reads only in kilometers, you have a problem. You could guess or use the conversion factor of 1 km/10 3 m. Look at the conversion below.

0.392 m × 1 km/10 m 3 = 0.392 × 10 3 km

= 3.92 × 10 –4 km

If you have centimeters and need to know the answer in inches, then use the conversion factor 1 inch/2.54 cm.

914 cm × 1 inch/2.54 cm = 360 inches (since 914 has 3 significant digits)

Converting measurements can also be a two-step process.

mg ⇒ g ⇒ kg

liters ⇒ quarts ⇒ gallons

miles per hour ⇒ meters per minute

Look at the two-step conversions below.

#### Example 1

2461 mg ⇒ kg

mg ⇒ g ⇒ kg

1 mg = 10 –3 g; 1 kg = 10 3 g (conversion factors)

2461 mg × 10 –3 g/mg × 1 kg/10 3 g

= 2461 × 10 –6 kg = 2.461 × 10 –3 kg

#### Example 2

8.47 liters ⇒ gallons

liters ⇒ quarts ⇒ gallons

1.06 qt/liters; 1 gal/4 qt (conversion factors)

8.47 liters × 1.06 qt/liter × 1 gal/4 qt = 2.24 gallons

#### Example 3

70 miles/hour ⇒ meters/minute

miles/hr ⇒ km/hr ⇒ m/hr ⇒ m/min.

1.61 km/mi; 10 3 m/km; 1 hr/60 min (conversion factors)

70 mi/hr × 1.61 km/mi × 10 3 m/km × 1 hr/60 min = 1878.33 m/min =

1.9 × 10 3 m/min

SI derived units are obtained by combining SI base units.

## Temperature

The measure of the intensity of heat of a substance is said to be its temperature . A thermometer measures temperature. Temperature is measured in three different units: Fahrenheit (°F) in the United States, Celsius (°C) in science and elsewhere, and Kelvin to measure absolute temperature. Figure 2.1 shows how the temperature systems compare.

Fig. 2.1. A comparison of the three temperature scales shows their differences clearly.

The conversion factor for Celsius to Fahrenheit is

t (F) = [ t (C) × 1.8F/1°C] + 32 = [ t (C) × 1.8] + 32

The conversion factor for Fahrenheit to Celsius is ( hint: subtract 32 so that both numbers start at the same temperature)

t (C) = [ t (F) − 32°F] × 1°C/1.8°F = [ t (F) − 32]/1.8

or a simpler way to state it is:

°C = 5/9 (°F − 32)

#### Example 1

A summer day in Hawaii might be 21°C. What is that in Fahrenheit?

21°C = 5/9 (°F − 32)

21 + 32 = 5/9°F

53 × 9 = 5°F

477/5 = 70°F

To obtain absolute zero (the lowest temperature possible), the kelvin scale is used, where the lowest temperature is zero. A kelvin is a SI temperature unit. The heat energy is zero.

To see how temperature conversion works, let’s convert normal body temperature, 98.6°F, to Celsius.

#### Example 2

°C = 5/9 (°F − 32)

°C = 5/9 (98.6°F − 32)

= 5/9 (66.6) = 37.0°C

°C can be converted to K by adding 273 to the Celsius temperature.

#### Example 3

K = °C + 273

K = 37°C + 273 = 310 K

Practice problems for these concepts can be found at - Science Experiment Data Practice Test

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