Worked examples
Two examples
Example 1
The formula: density = mass ÷ volumeA bar of soap has a mass of 120 grams and a volume of 100 cubic centimeters. What is its density?
- Step 1, write the formula: density = mass ÷ volume.
- Step 2, put in the numbers with their units: density = 120 g ÷ 100 cm³.
- Step 3, calculate: 120 ÷ 100 = 1.2. The units divide the same way, so the answer is in grams per cubic centimeter: 1.2 g/cm³.
- Step 4, check. Water’s density is about 1 g/cm³, and things denser than water sink. At 1.2, the soap should sink in a sink full of water, and soap does. The answer makes sense.
Answer: 1.2 g/cm³
Example 2
The formula: speed = distance ÷ timeA subway train travels 6 kilometers in 12 minutes. What is its average speed in kilometers per hour?
- Step 1, write the formula: speed = distance ÷ time.
- Step 2, get the units to match the question. It asks for kilometers per hour, but the time is in minutes. 12 minutes is 12 of the 60 minutes in an hour: 12 ÷ 60 = 0.2 hour.
- Step 3, calculate: 6 km ÷ 0.2 h = 30 km/h.
- Step 4, check: 30 kilometers per hour is a believable speed for a subway train. If you had divided 6 by 12 and written 0.5 km/h, the train would be slower than a person walking, and the check would catch it.
Answer: 30 km/h
Where this is taught: Science Practices, part 6: Numbers and units in science · Look Again Quiz 6: Numbers in Science
In your Kaplan book: Unit 4, Chapter 1, Lesson 6: Apply Scientific Formulas · Map of the Terrain, topic 6: Numbers in science
The drill
Ten questions
How many:
Read what is in the box first, if there is one. Then tap your answer; a few questions ask you to choose words from a drop-down instead, the way the GED test does. Press Check my answers at the bottom.Read what is in the box first, if there is one. Circle your answer; where there are brackets, circle the choice that fits. The answer key, with the reasoning, is on the last page.