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D.4 Multiply whole numbers by powers of ten

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What does it mean to multiply by powers of ten?

Powers of ten are numbers like 10, 100, 1,000, and so on. Each power of ten has one more zero than the one before it. When you multiply a whole number by a power of ten, you make the number ten times larger for each zero in the power of ten.

Examples:
  • 4 × 10 = 40
  • 4 × 100 = 400
  • 4 × 1,000 = 4,000
Note

Each time you multiply by ten, the digits move one place to the left. This makes the number ten times greater.

Understanding powers of ten

A power of ten can be written using an exponent. The exponent tells how many times to multiply 10 by itself.

Examples:
  • 10¹ = 10
  • 10² = 10 × 10 = 100
  • 10³ = 10 × 10 × 10 = 1,000
Note

The exponent shows how many zeros follow the 1 when writing the number as a whole number.

How to multiply whole numbers by powers of ten

When multiplying a whole number by a power of ten, move each digit one place to the left for every zero in the power of ten. You can also think of this as adding zeros to the end of the number.

Steps:
  • Start with the number 6.
  • Multiply by 10: 6 × 10 = 60.
  • Multiply by 100: 6 × 100 = 600.
  • Multiply by 1,000: 6 × 1,000 = 6,000.
Note

Each zero in the power of ten means the number is ten times greater. The digits do not change—only their place value does.

Using exponents to describe multiplication by powers of ten

Exponents make it easier to show repeated multiplication by ten. For example, multiplying by 10³ means multiplying by 1,000.

Examples:
  • 7 × 10² = 7 × 100 = 700
  • 25 × 10³ = 25 × 1,000 = 25,000
  • 3 × 10⁴ = 3 × 10,000 = 30,000
Note

Remember: the exponent tells how many zeros to add after the number when multiplying whole numbers by powers of ten.

Why multiplying by powers of ten matters

Understanding how to multiply by powers of ten helps you work with large numbers, convert units, and understand place value in more advanced math and science.

Example:
  • 50 × 10 = 500 (ten times greater)
  • 50 × 100 = 5,000 (one hundred times greater)
Note

This skill will help you estimate, measure, and compute more efficiently in real-world math situations.