Powers of 10 chart
A power of 10 is 10 multiplied by itself some number of times. The exponent says how many times, and it is also how many zeros follow the 1: 10³ is 10 × 10 × 10, which is 1,000.
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What is on the sheet
Powers of 10
| Power | Number | Zeros | Name |
|---|---|---|---|
| 10⁰ | 1 | 0 | one |
| 10¹ | 10 | 1 | ten |
| 10² | 100 | 2 | one hundred |
| 10³ | 1,000 | 3 | one thousand |
| 10⁴ | 10,000 | 4 | ten thousand |
| 10⁵ | 100,000 | 5 | one hundred thousand |
| 10⁶ | 1,000,000 | 6 | one million |
| 10⁷ | 10,000,000 | 7 | ten million |
| 10⁸ | 100,000,000 | 8 | one hundred million |
| 10⁹ | 1,000,000,000 | 9 | one billion |
Powers of 10 less than one
| Power | Decimal | Fraction | Name |
|---|---|---|---|
| 10⁻¹ | 0.1 | 1/10 | one tenth |
| 10⁻² | 0.01 | 1/100 | one hundredth |
| 10⁻³ | 0.001 | 1/1,000 | one thousandth |
Multiplying and dividing by powers of 10
| Problem | Answer | The decimal point moves |
|---|---|---|
| 4.7 × 10 | 47 | 1 place to the right |
| 4.7 × 100 | 470 | 2 places to the right |
| 4.7 × 1,000 | 4,700 | 3 places to the right |
| 4.7 ÷ 10 | 0.47 | 1 place to the left |
| 4.7 ÷ 100 | 0.047 | 2 places to the left |
| 4.7 ÷ 1,000 | 0.0047 | 3 places to the left |
| 52 × 10³ | 52,000 | 3 places to the right |
The pattern in the zeros
Each row of the first table is 10 times the row above it, so each one has one more zero. That makes the exponent easy to read: count the zeros after the 1 and you have it. 1,000,000 has six zeros, so it is 10⁶. 10⁰ is 1 because it has no zeros at all.
The same pattern runs the other way. Each row of the second table is a tenth of the one above it, so the exponents carry on below zero: 10⁻¹ is one tenth, 10⁻² one hundredth. 8th grade uses these to write very small numbers in scientific notation.
Moving the decimal point
Multiplying by 10 makes every digit worth ten times as much, so the digits shift one place to the left and the decimal point ends up one place further right. Multiplying by 100 or 10² moves it two places, by 1,000 or 10³ three places, and dividing moves it the other way. When there are no digits left to move past, write zeros: 52 × 10³ is 52,000.
5th grade explains these patterns and writes powers of 10 with whole-number exponents (CCSS 5.NBT.A.2). 6th grade evaluates exponents in general (6.EE.A.1), and 8th grade works with integer exponents and scientific notation (8.EE.A.1, 8.EE.A.3).
Common questions
- Why is 10 to the power of 0 equal to 1?
- Each step down the table divides by 10: 1,000, 100, 10, and then 10 divided by 10, which is 1. The pattern only works if 10⁰ is 1.
- How many zeros are in a billion?
- Nine. A billion is 1,000,000,000, which is 10⁹. A million has six zeros and a thousand has three.