Use Patterns to Divide by Powers of Ten

Patterns for Dividing with Decimals

Lesson 6.1

Remember:

1 = 10⁰

10 = 10¹

100 = 10²

1000 = 10³

Find 89.5 ÷ 10

• A number divided by 10 is less than the number.

• Moving the decimal point to the left decreases the number's value.

• Place value is based on 10, so dividing by 10 has the same result as moving the decimal point one place to the left.

Notice the patterns in the table.

• 89.5 ÷ 10

• 10 = 10¹

• The exponent tells us to move the decimal point one place.

• Since we are dividing, we move the decimal point one place to the left.

• So, 89.5 ÷ 10 = 8.95

Try It!

Suppose you have a rope that is 293.5 cm long.

If you cut the rope into 10¹ equal pieces, how long would each piece be?

Multiple Choice

293.5 ÷ 10¹

• 29.35

• 2.935

• 2,935

Look for a pattern.

4,600 ÷ 10 = 460

460 ÷ 10 = 46

46 ÷ 10 = 4.6

4.6 ÷ 10 = 0.46

Look for a pattern.

134.4 ÷ 10³ = 0.1344

134.4 ÷ 10² = 1.344

134.4 ÷ 10¹ = 13.44

134.4 ÷ 10⁰ = 134.4

Let's Practice

Use mental math to find each quotient.

Multiple Choice

370.2 ÷ 10²

• 37.02

• 3.702

• 0.3702

Multiple Choice

7.25 ÷ 10

• 0.725

• 72.5

• 725

Multiple Choice

28.14 ÷ 10⁰

• 28.14

• 2.814

• 281.4

Multiple Choice

3,642.4 ÷ 10²

• 364.24

• 36.424

• 3,642.40

Multiple Choice

15.7 ÷ 1,000

• 1.57

• 0.157

• 0.0157