1/15
00:00

AA.1 Divide decimals by powers of ten

Loading questions...

What does it mean to divide decimals by powers of ten?

When you divide a decimal by a power of ten (10, 100, 1000, etc.), you move the decimal point to the left. Each zero in the power of ten tells you how many places to move it.

Examples:
  • 4.5 ÷ 10 = 0.45
  • 4.5 ÷ 100 = 0.045
  • 4.5 ÷ 1000 = 0.0045
Note

Each time you divide by 10, the value becomes ten times smaller. Dividing by 100 makes it one hundred times smaller, and so on.

Understanding powers of ten

A power of ten is any number that can be written as 10 raised to an exponent. For example, 10¹ = 10, 10² = 100, and 10³ = 1000. The exponent tells you how many zeros are in the number.

Examples:
  • 10¹ = 10
  • 10² = 100
  • 10³ = 1000
Note

Powers of ten are important because they show the pattern of place value shifts when multiplying or dividing decimals.

How to divide decimals by powers of ten

To divide a decimal by a power of ten, move the decimal point to the left for each zero in the power of ten. No actual division is needed — just shift the digits.

Steps:
  • Identify how many zeros are in the divisor (10, 100, 1000, etc.).
  • Move the decimal point to the left that many places.
  • Fill in zeros if needed to hold place values.
Note

Dividing by 10 moves the decimal one place left; dividing by 100 moves it two places; dividing by 1000 moves it three places, and so on.

Examples in real-world situations

Understanding how to divide decimals by powers of ten helps with money, measurement, and scientific notation. It is a key part of understanding place value relationships.

Examples:
  • A length of 4.5 meters divided by 10 equals 0.45 meters (ten times smaller).
  • A price of $56.7 divided by 100 equals $0.567 (hundred times smaller).
  • A measurement of 0.8 divided by 10 equals 0.08.
Note

Think of dividing by powers of ten as shifting each digit’s place value to a smaller position (tenths → hundredths → thousandths, etc.).

Check your understanding

Before solving problems, ask yourself: “How many places should the decimal move?” This helps you reason through the problem instead of just memorizing steps.

Quick Practice:
  • 6.3 ÷ 10 = ?
  • 2.75 ÷ 100 = ?
  • 0.48 ÷ 1000 = ?
Note

Check your answers by reversing the process — multiply by the same power of ten to see if you get back to the original number.