# LESSON 4 – DIVIDING DECIMALS BY 10, 100, 1000

Objective:

At the end of this lesson, students should be able to divide decimals by multiples of ten.

When dividing decimal numbers by multiples of 10, the place value of the digits change, the number becomes smaller. The place value of the digits move from left to right making it look like the position of the decimal point moves from right to the left according to the number of zeros dividing the decimal number. In the real sense, it is the position of the digits that change.

Example 1

48.31 ¸ 10

Solution

48.31 ¸ 10 = 4.831

It looks like the position of the decimal point moves one step to the left because 10 has one zero but in reality, it is the digits that change position. The value of the 8 has changed from 8units to 8-tenths; the value of the 3 has changed from 3/10 to 3/100 and so on. The answer 4.831 is 10 times smaller than 48.31.

Example 2

53.64 ¸ 100

Solution

53.64¸ 100 = 0.5364

It looks like the position of the decimal point moves two steps to the left because 100 has two zeros but in reality, it is the digits that change position. The value of the 5 has changed from 50 to 5-tenths, the value of the 3 has changed from 3 units to 3/100 and so on. The number becomes 100 times smaller.

Example: 3

4.973 ÷ 1000 = 0.004973

From the example above, the multiple of 10 was 1000 having three zeros therefore all the digits will move 3 places to the left, making it look as if the decimal point has moved three steps to the left.

Where there are no counting numbers after the movement, a zero is placed behind the last counting number to avoid confusion as shown above.

Unit 5 Lesson 4: Exercise 1

Try these

1) 99 ¸ 100

2) 54 ¸ 10

3) 5 ¸ 1000

4) 025 ¸ 10

5) 823 ¸100

6) 7 ¸ 1000

7) 5 ¸ 100

8) 9 ¸ 1000

9) 077 ¸10

10) 8 ¸ 100

Unit 5 Lesson 4: Exercise 2

Now try these

1) 411 ¸ 10

2) 76.07 ¸ 100

3) 1 ¸ 1000

4) 0173 ¸ 100

5) 11 ¸ 10

6) 113 ¸ 1000

7) 137 ¸ 10

8) 3611 ¸ 100

9) 315 ¸ 1000

10) 4730 ¸ 100

Unit 5 Lesson 4: Exercise 3

Now try these

1) 196 ¸ 10

2) 98 ´ 10

3) 3607 ´ 100

4) 39 ÷ 1000

5) 8 ÷ 100

6) 0795 × 10

7) 865 × 1000

8) 549 ÷ 1000

9) 285 × 10

10) 0671 ÷ 10

Unit 5 Lesson 4: Exercise 4

Copy and complete the table below.

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