How to Read and Write Small Numbers
The Math Dude explains using scientific notation to read and write small numbers.
Jason Marshall, PhD
We’ve talked before about how to use scientific notation to make it easier to read and write large numbers. For example, we can use the idea that 103 is the number you get when you move the decimal point in 1.0 three positions to the right (giving 1,000), to see that we can write a really large number like 300,000,000 in scientific notation as 3×108. One of the main advantages of using scientific notation to write large numbers like this is that you don’t have to worry about writing out all those zeros!
As luck would have it, we learned this week that the same thing is true when using scientific notation to write very small numbers. For example, the exponent –3 in an expression like 10–3 tells us to move the decimal point in 1.0 three positions to the left to get 0.001. We can use this same idea to write a really small number like 0.000000005 in scientific notation as 5×10-9 and get rid of all those hard-to-keep-track-of zeros. With that in mind, here are the answers to this week’s practice problems:
- 0.005 = 5×10-3
- 0.00072 = 7.2×10-4
- 0.0000000823 = 8.23×10-8
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About the Author
Jason Marshall is the author of The Math Dude’s Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.