# Division by 10s, 100s, 1000s

### How do you divide numbers by 10, 100 and 1000?

Dividing by 10

When you divide a number by 10, the value of each of its digits decreases ten times. Hence, the value of the whole number decreases ten times.

Example:

Quite simply,

460 ÷ 10 = 46 tens ÷ 10
= 46

460 ÷ 10 = (400 + 60) ÷ 10

= (400 ÷ 10) + (60 ÷ 10)

= 40 + 6

= 46

Dividing by 100

When you divide a number by 100, the value of each of its digits decreases hundred times. Hence, the value of the whole number decreases hundred times.

Example:

Quite simply,

4600 ÷ 100 = 46 hundreds ÷ 100
= 46

4600 ÷ 100 = (4000 + 600) ÷ 100

= (4000 ÷ 100) + (600 ÷ 100)

= 40 + 6

= 46

Dividing by 1000

When you divide a number by 1000, the value of each of its digits decreases thousand times. Hence, the value of the whole number decreases thousand times.

Example:

Quite simply,

46000 ÷ 1000 = 46 thousands ÷ 1000
= 46

46 000 ÷ 1000 = (40 000 + 6 000) ÷ 1000

= (40 000 ÷ 1000) + (6 000 ÷ 1000)

= 40 + 6

= 46

### If 430000 ÷ 2 = 215000, find the value of 430000 ÷ 20, 430000 ÷ 200 and 430000 ÷ 2000.

1. 430000 ÷ 20 = 430 000 ÷ (2 × 10)

= 430 000 ÷ 2 ÷ 10

= (430 000 ÷ 2) ÷ 10

= 215 000 ÷ 10

= 21 500

2. 430000 ÷ 200 = 430 000 ÷ (2 × 100)

= 430 000 ÷ 2 ÷ 100

= (430 000 ÷ 2) ÷ 100

= 215 000 ÷ 100

= 2150

3. 430000 ÷ 2000 = 430 000 ÷ (2 × 1000)

= 430 000 ÷ 2 ÷ 1000

= (430 000 ÷ 2) ÷ 1000

= 215 000 ÷ 1000

= 215

### Estimate the value of 782 ÷ 23 and 9123 ÷ 32.

782 ≈ 800

and

23 ≈ 20
1. 782 ÷ 23 ≈ 800 ÷ 20

= 800 ÷ (2 x 10)

= 800 ÷ 2 ÷ 10

= (800 ÷ 2) ÷ 10

= 400 ÷ 10

= 40

2. 9123 ≈ 9000

and

32 ≈ 30
3. 9123 ÷ 32 ≈ 9000 ÷ 30

= 9000 ÷ (3 x 10)

= 9000 ÷ 3 ÷ 10

= (9000 ÷ 3) ÷ 10

= 300 ÷ 10

= 30