Mentally Dividing Decimal Numbers by 10 and by 100
Dividing decimal numbers mentally by 10 or 100 uses a simple decimal point shift: dividing by 10 moves the decimal point one place left, dividing by 100 moves it two places left. In Grade 6 Saxon Math Course 1, 34.7 ÷ 10 = 3.47 and 34.7 ÷ 100 = 0.347. This shortcut works because our base-10 number system reduces each digit's value by one-tenth for every step left. The same rule extends to dividing by powers of 10 (10ⁿ shifts the decimal n places left).
Key Concepts
New Concept When we divide a decimal number by 10 or by 100, the quotient has the same digits as the dividend. To find the quotient, we simply move the decimal point.
To divide by 10 , move the decimal point one place to the left . To divide by 100 , move the decimal point two places to the left . What’s next This is a foundational skill for working with powers of ten. Now, you'll apply this rule with worked examples and practice problems to build speed and accuracy.
Common Questions
What is the rule for dividing a decimal by 10?
Move the decimal point one place to the left. Example: 5.6 ÷ 10 = 0.56.
What is 34.7 ÷ 100?
Move decimal two places left: 0.347.
What is 0.85 ÷ 10?
Move decimal one place left: 0.085.
Why does dividing by 10 move the decimal point left?
Each place to the left is worth one-tenth less. Dividing the number by 10 decreases every digit's place value by one step, shifting the decimal left.
How do you divide by 1,000 mentally?
Move the decimal point three places to the left. Example: 52.3 ÷ 1,000 = 0.0523.