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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