The document explains the importance of converting units in contexts like chemistry and everyday scenarios, highlighting the use of conversion factors. It outlines steps to convert units through examples, detailing how to handle measurements and ensuring proper unit cancellation. Additionally, it covers more complex conversions involving squared or cubed units.

1. Converting Units

2. Why do we need to convert? Sometimes, we aren’t able to make a measurement in the units we want to use. In Chemistry and Physics, we use equations to solve problems. These equations only work when certain units are used. In your everyday life, you might need to convert units. For example, maybe you want to compare prices of products at the grocery store. Unless the volume of each product is listed in the same unit, we won’t be able to compare prices.

3. Conversion Factors When we convert units, we use conversion factors. Conversion factors are relationships between units that we know to be true. Some examples: 12 inches = 1 foot 1 minute = 60 seconds 16 ounces = 1 lb 24 hours = 1 day

4. Steps to converting units: Write the number (with units) that you want to convert. Multiply it by a conversion factor, written as a fraction. Make sure the old units cancel. Multiply all the numbers on the top and divide by the numbers on the bottom.

5. Example Problem How many inches in 4.3 feet? 1) Write the number (with units) that you want to convert. 2) Multiply it by a conversion factor, written as a fraction. Make sure the unit that you want to convert from is on the bottom and the unit you want to convert to is on the top. 3) Make sure the old units cancel. 4) Multiply all of the numbers on the top and divide by all of the numbers on the bottom to find your answer. 4.3 ft 4.3 ft X 12 in 1 ft 4.3 ft X 12 in 1 ft 4.3 ft X 12 in 1 ft = 51.6 in

6. Another Example 1) Write the number (with units) that you want to convert. 2) Multiply it by a conversion factor, written as a fraction. Make sure the unit that you want to convert from is on the bottom and the unit you want to convert to is on the top. 3) Make sure the old units cancel. 4) Multiply all of the numbers on the top and divide by all of the numbers on the bottom to find your answer. Convert 52.8 hours to days. 52.8 hrs 52.8 hrs X 1 day 24 hrs 52.8 hrs X 1 day 24 hrs 52.8 hrs X 1 day 24 hrs = 2.2 days

7. What if there are two units to change? 3.45 m/min = ___________ ft/s We need to change meters to feet. (1 meter = 3.281 feet) We also need to change minutes to seconds. (1 minute = 60 seconds) Choose one unit to change first. Then, multiply by a second fraction to change the other. Notice: The original number was written with minutes on the bottom. The only units which didn’t cancel were the units we wanted to convert to. We arrived at the answer by multiplying 3.45 X 3.281 and dividing by 60. 3.45 m min X 3.281 ft 1 m X 1 min 60 s = 0.189 ft/s

8. What if one or more of the units is squared or cubed? An object has an area of 45 cm . What is its area measured in square inches? 2 This problem should be set-up as if you are just converting centimeters to inches. (2.54 cm = 1 in) Next, place parentheses around the entire conversion factor and square it. This will square all numbers and units inside the parentheses. Finally, instead of dividing 45 by just 2.54, you’ll need to divide 45 by 2.54 squared . In other words, 45 divided by 2.54 divided by 2.54. 45 cm X 2 1 in 2.54 cm 45 cm X 2 1 in 2.54 cm ( ) 2 45 cm X 2 1 in 2.54 cm ( ) 2 = 6.98 in 2