Worked examples
Two examples
Example 1
Light travels about 3 × 108 meters per second. Write that as an ordinary number.
- Scientific notation writes a number as a number from 1 to 10, times 10 to a power. The power, the small raised number, is called the exponent.
- The exponent here is 8, a positive number. A positive exponent means a large number: move the decimal point to the right.
- Start with 3, and move the decimal point 8 places to the right, writing a zero for each new place: 3 → 30 → 300 → … → 300,000,000.
- Count the places one at a time. Moving 7 places instead of 8 is the most common mistake.
Answer: 300,000,000
Example 2
A red blood cell is about 0.000008 meter wide. Write that in scientific notation.
- Move the decimal point until the number is at least 1 and less than 10. Here that number is 8.
- Count how many places the decimal point moved to get from 0.000008 to 8: six places, to the right.
- Because the original number is small (less than 1), the exponent is negative: −6.
- So 0.000008 = 8 × 10−6. A negative exponent does not mean the number is below zero; it means it is very small.
Answer: 8 × 10−6
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.