Decimal Operations

Study Sheet

Decimal Operations

Multiplying and dividing decimals

Counting Decimal Places

Concept
The Big Idea

Multiply as if the points were not there, then put the point back. The answer has as many decimal places as the two factors have together.

Example
Finding 2.4×32.4 \times 3

Ignore the point: 24×3=7224 \times 3 = 72. There was one decimal place, so the answer is 7.27.2.

Tip
Sanity check

2.42.4 is close to 22, so the answer should be near 66 — and 7.27.2 is. A misplaced point would give 0.720.72 or 7272, both clearly wrong.

In Plain Terms & More Examples

Concept
In plain terms

Multiply as if the points were not there, then count how many decimal places the two numbers had together and put the point back that far from the right.

Example
Finding 1.5×41.5 \times 4

Ignore the point: 15×4=6015 \times 4 = 60. One decimal place, so the answer is 6.06.0.

Example
Finding 0.3×0.20.3 \times 0.2

Ignore the points: 3×2=63 \times 2 = 6. Two decimal places, so the answer is 0.060.06.

Example
A multi-step problem

You buy 33 notebooks at $2.40\$2.40 each and pay with a $10\$10 bill. Step 1: 3×2.40=7.203 \times 2.40 = 7.20. Step 2: the change is 10−7.20=$2.8010 - 7.20 = \$2.80.