Multiplication by 10s, 100s, 1000s

1. Multiply 46 by 10.

Multiplying by 10

When you multiply a number by 10, the value of each of its digits increases ten times. Hence, the value of the whole number increases ten times.
     46  ×  10
=  (40 + 6)  ×  10
=  (40  ×  10)  +  (6  ×  10)
=  400  +  60
=  460
Quite simply,
    46  ×  10
=  46 tens
=  460

2. Multiply 46 by 100.

Multiplying by 100

When you multiply a number by 100, the value of each of its digits increases hundred times. Hence, the value of the whole number increases hundred times.
     46  ×  100
=  (40 + 6)  ×  100
=  (40  ×  100)  +  (6  ×  100)
=  4000  +  600
=  4600
Quite simply,
    46  ×  100
=  46 hundreds
=  4600

3. Multiply 46 by 1000.

Multiplying by 1000

When you multiply a number by 1000, the value of each of its digits increases thousand times. Hence, the value of the whole number increases thousand times.
     46  ×  1000
=  (40 + 6)  ×  1000
=  (40  ×  1000)  +  (6  ×  1000)
=  40000  +  6000
=  46000
Quite simply,
    46  ×  1000
=  46 thousands
=  46000

4. If 430  ×  2 = 860, find the value of:
a)  430  ×  20
b)  430  ×  200
c)  430  ×  2000

a)        430  ×  20
       =  430  ×  2  ×  10
       =  (430  ×  2)  ×  10
       =  860  ×  10
       =  8600
b)        430  ×  200
       =  430  ×  2  ×  100
       =  (430  ×  2)  ×  100
       =  860  ×  100
       =  86 000
c)        430  ×  2000
       =  430  ×  2  ×  1000
       =  (430  ×  2)  ×  1000
       =  860  ×  1000
       =  860 000

5. Estimate the value of:
a)  782  ×  23
b)  42  ×  9123

a)        782  ×  23
       ≈  800  ×  20
       =  800  ×  2  ×  10
       =  1600  ×  10
       =  16 000
782  ≈  800
and
23  ≈  20
b)        42  ×  9123
       ≈  40  ×  9000
       =  40  ×  9  ×  1000
       =  360  ×  1000
       =  360 000
42  ≈  40
and
9123  ≈  9000