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Multiplying Decimals

Overview

Counting the hops.

What is it?

Multiplying numbers with dots.

History

Essential for calculating tax and discounts.

Key Idea

Ignore the decimals, multiply normally, then put the dot back by counting total decimal places.

Practice This Topic

Concept Guide

Plain English: Pretend the decimals don't exist. Multiply 0.5 x 0.3 as if it was 5 x 3 (which is 15). Then count how many numbers were behind decimals (2). Move the dot 2 spots left. Answer: 0.15.

Real-world example: Calculating 8.25% sales tax on a $19.99 item.

How to do it

  1. Ignore dots.
  2. Multiply.
  3. Count total decimal places in original problem.
  4. Move dot in answer that many steps left.
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Common Pitfall

Lining up the dots like addition. DO NOT line up the dots! Line up the right wall.

Word Problem
"Gas costs $3.50 a gallon. You pump 10.5 gallons."
Reasoning: 350 x 105 = 36750. Total decimals = 3 (2 from price, 1 from gas). Move dot 3 times -> $36.75.

Practice Examples

Counting Hops
0.2 (1 hop) x0.3 (1 hop) ---- 0.06 (2 hops)
2x3=6. Move dot twice.