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AA.3 Divide by 0.1, 0.01, or 0.001

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Divide by 0.1, 0.01, or 0.001

Dividing by a decimal such as 0.1, 0.01, or 0.001 means finding how many of those decimal parts fit into a number. Smaller decimals fit more times, so the result becomes larger.

Examples:
  • 8 ÷ 0.1 means: how many tenths are in 8?
  • 5 ÷ 0.01 means: how many hundredths are in 5?
  • 3 ÷ 0.001 means: how many thousandths are in 3?
Note

The smaller the decimal you divide by, the bigger the quotient becomes.

How does dividing by 0.1, 0.01, or 0.001 work?

To divide by these decimals, you can multiply the number by 10, 100, or 1,000. This works because dividing by a decimal less than 1 is the same as multiplying by a whole number.

Examples:
  • 12 ÷ 0.1 = 12 × 10 = 120
  • 4.5 ÷ 0.01 = 4.5 × 100 = 450
  • 0.32 ÷ 0.001 = 0.32 × 1,000 = 320
Note

Think of it this way: dividing by 0.1 means “How many tenths make this number?” Since ten tenths make one whole, you multiply by 10.

Using place value to understand division

Each decimal place represents smaller parts of one whole. Understanding tenths, hundredths, and thousandths helps explain why the quotient increases when dividing by a smaller decimal.

Example:
  • 1 whole = 10 tenths → dividing by 0.1 multiplies by 10
  • 1 whole = 100 hundredths → dividing by 0.01 multiplies by 100
  • 1 whole = 1,000 thousandths → dividing by 0.001 multiplies by 1,000
Note

Picture the number of smaller units inside a whole. The more units there are, the more times they fit into a number.

Dividing by decimals in real-world situations

Dividing by decimals often comes up when measuring or splitting quantities into very small equal parts.

Examples:
  • If a ribbon is 6 meters long, and each piece is 0.1 meters, then 6 ÷ 0.1 = 60 pieces.
  • If a scientist measures 0.01 liters at a time from a 2-liter container, they can measure 2 ÷ 0.01 = 200 small samples.
  • If a machine cuts sheets 0.001 meters thick from a 1-meter board, it can cut 1 ÷ 0.001 = 1,000 sheets.
Note

Real-world problems often require careful unit reading so you divide by the correct decimal amount.

Common mistakes and how to avoid them

Students sometimes mix up dividing by decimals with multiplying by decimals. Remember that dividing by a decimal less than one makes the number larger.

Examples:
  • Incorrect: 7 ÷ 0.1 = 0.7
  • Correct: 7 ÷ 0.1 = 70
  • Tip: Compare 0.1 to 1. Since 0.1 is smaller, the quotient should be larger.
Note

You can always check your answer by multiplying the quotient by the divisor to see if it equals the original number.