Study Guide

Fractions & Decimals - Multiplying Decimals

Multiplying Decimals

Multiplying decimals
is only slightly more complicated than adding and subtracting decimals. The good news is that we don't need to worry about lining up the decimal points. In fact, we don't even need to think about the decimal points until the final step. 

How to Multiply Decimals

  1. Stack the two numbers like usual, with both numbers aligned on the right-hand side.
  2. Multiply like usual, ignoring all decimal points.
  3. To place the decimal point in our final answer, count how many total numbers are behind (to the right of) the decimals in both of the original numbers and add them together.
  4. In your answer, starting from the right, move the decimal that many places to the left.

Let's see these steps in action.

Sample Problem

What is 8.096 × 0.7?

First we stack the numbers. Warning: do not line up the decimal points.

×      0.7

Then we pretend those decimal points don't exist, and multiply like normal.

×      0.7

Notice the invisible fancy footwork it took to multiply these? But in the end we get the answer 56672 with a decimal point in it somewhere. The first number has three digits to the right of the decimal, and the second number has one digit to the right of the decimal. Together that's four digits, so the decimal starts to the right of the 2 and goes four places to the left.

×      0.7

It's not as easy as Tetris, but it feels somehow similar.

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