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C.2 Find the value of powers of ten

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What are powers of ten?

Powers of ten are numbers that can be written as 10 raised to an exponent. The exponent tells us how many times to multiply 10 by itself.

Examples:
  • 10² means 10 × 10 = 100
  • 10³ means 10 × 10 × 10 = 1,000
  • 10⁴ means 10 × 10 × 10 × 10 = 10,000
Note

Any number raised to the power of 1 equals itself. So 10¹ = 10.

How to find the value of powers of ten

To find the value of a power of ten, multiply 10 by itself as many times as the exponent indicates.

Steps:
  • Look at the exponent (the small number)
  • Write 10 that many times with multiplication signs between them
  • Multiply to find the answer
Note

The exponent tells you how many zeros will be in your final answer. For example, 10⁵ = 100,000 (five zeros).

Common powers of ten you should know

Here are some of the most common powers of ten you will use in mathematics:

Power of Ten List:
  • 10¹ = 10
  • 10² = 100
  • 10³ = 1,000
  • 10⁴ = 10,000
  • 10⁵ = 100,000
  • 10⁶ = 1,000,000
Note

10⁰ (ten to the zero power) equals 1. This is a special rule for all numbers raised to the zero power.

Using powers of ten with place value

Powers of ten help us understand our place value system. Each place value is ten times greater than the place to its right.

Examples:
  • Thousands place: 1,000 = 10³
  • Hundreds place: 100 = 10²
  • Tens place: 10 = 10¹
  • Ones place: 1 = 10⁰
Note

When we move one place to the left, we multiply by 10. When we move one place to the right, we divide by 10.

Patterns in powers of ten

There are helpful patterns that make working with powers of ten easier to understand and remember.

Pattern Examples:
  • Each power of ten is 10 times greater than the previous one
  • The number of zeros equals the exponent
  • Multiplying by 10ⁿ moves the decimal point n places to the right
Note

When multiplying a decimal by a power of ten, count the zeros in the power of ten and move the decimal point that many places to the right.