Lesson 52: Mentally Dividing Decimal Numbers by 10 and by 100

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.

Property

When we divide by 10, the decimal point moves one place to the left.

Examples

$37.5 \div 10 = 3.75$
$87.5 \div 10 = 8.75$
$2.5 \div 10 = 0.25$

Explanation

Think of dividing by 10 as a simple one-step slide to the left for the decimal point. This mental shortcut makes the number 10 times smaller without any long division. The digits stay the same, but their place value shifts, giving you the correct answer instantly. It’s a math magic trick for making division easy and fast!

Property

When we divide by 100, the decimal point moves two places to the left.

Examples

$87.5 \div 100 = 0.875$
$25 \div 100 = 0.25$
$12.5 \div 100 = 0.125$

Explanation

Dividing by 100 is like doing the 'divide by 10' slide twice! The decimal point simply hops two places to the left, making the number 100 times smaller. Imagine the digits marching two spots to the right to their new, smaller place values. This is a powerful shortcut to handle division by 100 mentally and avoid calculators.