Powers of 10: Meaning, Facts, Examples
Shivam Singh26 Oct, 2025
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What Does Powers of 10 Mean?
Powers of 10 mean writing numbers using exponents where the base number is always 10. When we multiply 10 by itself again and again, we can show it in a shorter way using exponents. For example, 10 × 10 × 10 can be written as 10³, which means “10 to the power of 3”. Here, 10 is called the base, and 3 is the exponent. The exponent tells us how many times 10 is multiplied by itself.
Therefore, the powers of 10 help us write large or small numbers quickly. If the exponent is positive, it shows how many zeros are added after 1. For example, 10⁶ = 1,000,000. But if the exponent is negative, it means the number gets smaller and moves after the decimal point. For example, 10⁻³ = 0.001. To learn more about the Powers of 10, keep reading.
Read More: Laws of Exponents
10 to the Power of 2
10 to the power of 2 means 10 is multiplied by itself two times. It is written as 10² and read as “10 raised to the power of 2” or “10 squared”. Here, 10 is the base, and 2 is the exponent. So, 10² = 10 × 10 = 100.
This shows that multiplying 10 two times gives us 100. It is called the second power of 10. Using exponents like this makes it easy to write and understand numbers without writing too many zeros.
10 to the Power of 3
10 to the power of 3 means 10 is multiplied by itself three times. It is written as 10³ and read as 10 raised to the power of 3 or 10 cubed. Here, 10 is the base, and 3 is the exponent. So, 10³ = 10 × 10 × 10 = 1000.
This is also called the third power of 10. It shows that when 10 is multiplied three times, the result is 1000. Using exponents like this helps us write large numbers in a shorter and clearer way.
Read More: Exponents and Powers
Powers of 10 Chart
A powers of 10 chart shows the values of 10 when it is raised to different powers. Positive powers of 10 give large numbers, while negative powers give small numbers less than 1. For example, 10⁵ = 10 × 10 × 10 × 10 × 10 = 100000. In fraction form, it can be written as 100000/1. On the other hand, 10⁻⁵ = 1/(10 × 10 × 10 × 10 × 10) = 0.00001, which is a very small number. In fraction form, it is 1/100000.
A powers of 10 chart helps you see these values efficiently, including both positive powers of 10 and negative powers of 10, making it easy to understand and use large and small numbers while solving maths problems. Find the detailed Powers of 10 Chart below.
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Powers of 10 Chart |
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Powers of 10 |
Expanded Form |
Decimal Form |
Fraction Form |
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10⁵ |
10 × 10 × 10 × 10 × 10 |
100,000 |
100,000/1 |
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10⁴ |
10 × 10 × 10 × 10 |
10,000 |
10,000/1 |
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10³ |
10 × 10 × 10 |
1,000 |
1,000/1 |
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10² |
10 × 10 |
100 |
100/1 |
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10¹ |
10 |
10 |
10/1 |
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10⁰ |
1 |
1 |
1/1 |
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10⁻¹ |
1 / 10 |
0.1 |
1/10 |
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10⁻² |
1 / (10 × 10) |
0.01 |
1/100 |
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10⁻³ |
1 / (10 × 10 × 10) |
0.001 |
1/1,000 |
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10⁻⁴ |
1 / (10 × 10 × 10 × 10) |
0.0001 |
1/10,000 |
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10⁻⁵ |
1 / (10 × 10 × 10 × 10 × 10) |
0.00001 |
1/100,000 |
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10⁻⁶ |
1 / (10 × 10 × 10 × 10 × 10 × 10) |
0.000001 |
1/1,000,000 |
Read More: Area and Perimeter
Positive Powers of 10
Positive powers of 10 are numbers where 10 is multiplied by itself one or more times. These powers give us large numbers, and some of them have special names. For example, 10² = 100 is called a hundred, and 10³ = 1,000 is called a thousand.
Using these names makes it easy to understand and talk about large numbers for students. Check the table below showing some positive powers of 10, their names, and SI prefixes:
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Positive Powers of 10 |
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Positive Powers of 10 |
Name |
Prefix (Symbol) |
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10¹ |
Ten |
Deca (D) |
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10² |
Hundred |
Hecto (H) |
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10³ |
Thousand |
Kilo (K) |
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10⁶ |
Million |
Mega (M) |
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10⁹ |
Billion |
Giga (G) |
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10¹² |
Trillion |
Tera (T) |
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10¹⁵ |
Quadrillion |
Peta (P) |
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10¹⁸ |
Quintillion |
Exa (E) |
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10²¹ |
Sextillion |
Zetta (Z) |
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10²⁴ |
Septillion |
Yotta (Y) |
Negative Powers of 10
Negative powers of 10 are used to write very small numbers. A negative exponent means we take the reciprocal of the number and then solve it like a positive power. For example, 10⁻³ = 1 / 10³ = 1 / (10 × 10 × 10) = 0.001.
Negative powers of 10 help us express smaller numbers in a simple way without writing too many zeros after the decimal point. To understand it better, check some negative powers of 10 with their names and symbols, here:
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Negative Powers of 10 |
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Negative Powers of 10 |
Name |
Prefix (Symbol) |
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10⁻¹ |
Tenth |
Deci (d) |
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10⁻² |
Hundredth |
Centi (c) |
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10⁻³ |
Thousandth |
Milli (m) |
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10⁻⁶ |
Millionth |
Micro (μ) |
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10⁻⁹ |
Billionth |
Nano (n) |
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10⁻¹² |
Trillionth |
Pico (p) |
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10⁻¹⁵ |
Quadrillionth |
Femto (f) |
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10⁻¹⁸ |
Quintillionth |
Atto (a) |
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10⁻²¹ |
Sextillionth |
Zepto (z) |
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10⁻²⁴ |
Septillionth |
Yocto (y) |
Read More: Basic Algebra
Calculating Powers of 10
Calculating powers of 10 is easy if you follow some simple rules. For example, 10³ ÷ 10² = 1000 ÷ 100 = 10. But when the exponents are very large, it is better to use exponent rules instead of writing all the zeros. Let's understand calculating powers of 10 in detail.
1. Adding and Subtracting Powers of 10: To add or subtract powers of 10, we take the smallest power as a common factor and then simplify. For example: 10⁵ + 10⁸ = 10⁵ (1 + 10³) = 10⁵ × 1001 = 100,100,000.
2. Multiplying Powers of 10: To multiply, we add the exponents if the base is the same. For example: 10⁵ × 10⁸ = 10⁵⁺⁸ = 10¹³.
3. Dividing Powers of 10: To divide, we subtract the exponents if the base is the same. For example: 10¹⁷ ÷ 10¹⁵ = 10¹⁷⁻¹⁵ = 10² = 100.
Read More: Componendo and Dividendo Rule
Powers of 10 Examples
Here are some solved powers of 10 examples to help you understand how it is used in solving different maths problems:
Example 1: Which of the following is equal to 1,000,000?
a.) 10⁵
b.) 10⁶
c.) 10⁷
Solution: The number 1,000,000 has 6 zeros. So, it can be written as the 6th power of 10. That is, 10⁶. Therefore, the correct answer is (b) 10⁶.
Example 2: Find the missing exponent: 10ⁿ = 100
a.) 1
b.) 2
c.) 0
Solution: 10² = 10 × 10 = 100. So, the missing exponent is 2. Therefore, the correct answer is (b) 2.
Example 3: True or False:
a.) 10 to the power of 3 is 1,000
b.) 10¹ means 1
Solution:
a) True, 10³ = 10 × 10 × 10 = 1,000
b) False, 10¹ = 10, not 1
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