Division by 10s, 100s, 1000s

1. Divide 460 by 10.

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.
     460  ÷  10
=  (400 + 60)  ÷  10
=  (400  ÷  10)  +  (60  ÷  10)
=  40  +  6
=  46
Quite simply,
    460  ÷  10
=  46 tens  ÷  10
=  46

2. Divide 4600 by 100.

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.
     4600  ÷  100
=  (4000 + 60)  ÷  100
=  (4000  ÷  100)  +  (600  ÷  100)
=  40  +  6
=  46
Quite simply,
    4600  ÷  100
=  46 hundreds  ÷  100
=  46

3. Divide 46000 by 1000.

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.
     46000  ÷  1000
=  (40000 + 6000)  ÷  1000
=  (40000  ÷  1000)  +  (6000  ÷  1000)
=  40  +  6
=  46
Quite simply,
    46000  ÷  1000
=  46 thousands  ÷  1000
=  46

4. If 430000 divided by 2 = 215000, find the value of:
a)  430000 divided by 20
b)  430000 divided by 200
c)  430000 divided by 2000

a)        430 000  ÷  20
       =  430 000  ÷  2  ÷  10
       =  (430 000  ÷  2)  ÷  10
       =  215 000  ÷  10
       =  21 500
b)        430 000  ÷  200
       =  430 000  ÷  (2  ×  100)
       =  430 000  ÷  2  ÷  100
       =  (430 000  ÷  2)  ÷  100
       =  215 000  ÷  100
       =  2150
c)        430 000  ÷  2000
       =  430 000  ÷  (2  ×  1000)
       =  430 000  ÷  2  ÷  1000
       =  (430 000  ÷  2)  ÷  1000
       =  215 000  ÷  1000
       =  215

5. Estimate the value of:
a)  782 divided by 23
b)  9123 divided by 32

a)        782  ÷  23
       ≈  800  ÷  20
       =  800  ÷  (2  ×  10)
       =  800  ÷  2  ÷  10
       =  (800  ÷  2)  ÷  10
       =  400  ÷  10
       =  40
782  ≈  800
and
23  ≈  20
b)        9123  ÷  32
       ≈  9000  ÷  30
       =  9000  ÷  (3  ×  10)
       =  9000  ÷  3  ÷  10
       =  (9000  ÷  3)  ÷  10
       =  3000  ÷  10
       =  300
9123  ≈  9000
and
32  ≈  30