# Dividing decimals by power of 10

### Dividing decimals by power of 10

#### Lessons

In this lesson, we will learn:

• How to move the decimal place when dividing decimals by powers of 10
• How to understand decimal division using base ten (block) models

Notes:

• In the last lesson, we learned that powers of ten represent the repeated multiplication (or repeated division) of the number 10.

• We learned that when multiplying decimals by powers of 10, we look at the power of 10 exponent or the number of zeroes it represents to move decimals places to the right.
• For dividing decimals by powers of 10, we will move the decimal to the left!
• When you divide any number by 1, it stays exactly the same—just like multiplying by 1
• When you divide by 10, 100, and 1000:

• If there are no more numbers when moving the decimal place to the left, fill those spaces with leading zeroes!

• We can also use base ten (block) models to divide decimals by powers of 10. There are two different models, depending on what represents one whole:
• If one whole is represented by a hundred block (square), each time you divide by 10, you turn your model into the next smaller type: from hundred square $\,$$\,$ ten stick $\,$$\,$ one square.

• If whole is represented by a thousand block (cube), each time you divide by 10, you turn your model into the next smaller type: from thousand cube [Symbol] hundred square $\,$$\,$ ten stick $\,$$\,$ one square.

• Introduction
Introduction to dividing decimals by powers of 10:
a)
How can we use base ten (block) models to show decimal division with powers of 10?

• 1.
Dividing decimals (tenths and hundredths) by using base ten (block) models
Using base ten (block) models, draw and solve the division statements where one whole is represented by a hundred block (square).
a)
4.0 ÷ 10 =

b)
0.5 ÷ 10 =

c)
3.2 ÷ 10 =

• 2.
Dividing decimals (thousandths) by using base ten (block) models
Using base ten (block) models, draw and solve the division statements where one whole is represented by a thousand block (cube).
a)
2 ÷ 1000 =

b)
1.6 ÷ 100 =

c)
0.57 ÷ 10 =

• 3.
Decimal division word problem
Looking at the division statement: 0.26 divided by 103
a)
How many decimal place values does the dividend 0.26 have?

b)
What number does 103 represent?

c)
How many places does the decimal point move? And in which direction?

d)
What is the answer to the division question? What is the smallest place value in the answer?

• 4.
Decimal division word problem (working backwards)
Write the decimal division equation by working backwards to find the original dividend:
a)
A number is divided by 10 and the result is 23.1 - what was the original number?

b)
A number is divided by 100 and the result is .039 - what was the original number?

c)
A number is divided by 1000 and the result is 461.785 - what was the original number?