Number & Operations in Base Ten

Multiplying & Dividing Decimals

Multiplying and dividing decimals to the hundredths place.

Intermediate20 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Prerequisites

Adding & Subtracting Decimals

Where Does the Decimal Point Land in a Product?

Before reading on, predict: how many decimal places should the answer to 0.3 × 0.2 have? Some people guess one, matching the numbers being multiplied — try working it out using what you know about fractions, and see if your prediction holds up.

0.3 is the same as 3/10, and 0.2 is the same as 2/10. Multiplying those fractions gives (3 × 2)/(10 × 10) = 6/100, which as a decimal is 0.06 — two decimal places, not one. The rule for decimal multiplication comes directly from this: the total number of decimal places in the answer equals the sum of the decimal places in the two numbers being multiplied.

Worked Example — Multiplying Two Decimals

Multiply 1.4 × 0.6. Multiply as if there were no decimal points at all: 14 × 6 = 84. Count the total decimal places in the original numbers: 1.4 has one, and 0.6 has one, for a total of two. Place the decimal point two places from the right in 84, giving 0.84.

Worked Example — Dividing a Decimal by a Decimal

Divide 4.8 ÷ 0.6. Multiplying both numbers by 10 turns the divisor into a whole number without changing the answer, since both parts of the division are scaled the same way: 48 ÷ 6 = 8. So 4.8 ÷ 0.6 = 8.

1.4 \times 0.6 = \dfrac{14}{10} \times \dfrac{6}{10} = \dfrac{84}{100} = 0.84

Tip

To divide by a decimal, multiply both the divisor and the dividend by the same power of ten until the divisor becomes a whole number — this doesn't change the answer, since multiplying both numbers by the same amount is the same as multiplying the whole division by 1.

Common Mistakes

Placing the decimal point in a product by matching the position from one of the original numbers, instead of counting total decimal places.
Count the decimal places in both original numbers and add them together — that total is exactly how many decimal places belong in the final product.
Multiplying only the dividend by a power of ten when dividing by a decimal, and not the divisor too.
Both the divisor and the dividend must be multiplied by the same power of ten together, so the value of the division itself stays exactly the same.

Key Takeaways

Multiplying decimals: multiply as whole numbers first, then place the decimal point using the total decimal places from both original numbers.
Dividing by a decimal: multiply both numbers by the same power of ten until the divisor is a whole number.
These rules come directly from what decimals actually represent as fractions with a denominator of 10, 100, or 1,000.

Summary

Decimal multiplication and division rules follow directly from decimals' fraction meaning. The next unit returns to fractions themselves, adding and subtracting ones whose denominators don't already match.

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