Mentally Multiplying Decimals
Multiplying decimal numbers by powers of 10 mentally uses a decimal-point shift: multiply by 10 moves the decimal one place right, multiply by 100 moves it two places right. In Grade 6 Saxon Math Course 1, 3.45 × 10 = 34.5 and 3.45 × 100 = 345. This shortcut works because multiplying by 10 increases each digit's place value by one step. Combined with the division shift rule (moving left), students can fluidly convert between forms in measurement, scientific notation, and mental arithmetic.
Key Concepts
Property To multiply a decimal by $10$, shift the decimal point one place to the right. To multiply by $100$, shift the decimal point two places to the right.
Examples $0.35 \times 10 = 3.5$ $2.5 \times 100 = 250$ $0.125 \times 100 = 12.5$.
Explanation Forget complex calculations! Multiplying a decimal by $10$ or $100$ is just a simple shift. While the digits are actually moving one or two places to the left to get bigger, the easiest way to see it is by moving the decimal point to the right. It’s the same result, but way faster for your brain!
Common Questions
What is the rule for multiplying a decimal by 10?
Move the decimal point one place to the right. Example: 2.7 × 10 = 27.
What is 3.45 × 100?
Move decimal two places right: 345.
What is 0.06 × 10?
Move decimal one place right: 0.6.
What is 1.5 × 1,000?
Move decimal three places right: 1,500.
Why does multiplying by 10 move the decimal right?
Multiplying by 10 increases every digit's place value by one step to the left, which is equivalent to moving the decimal point one place to the right.