1. Multiplying by powers of 10 Decimals

2. POWERS of 10 with DECIMALS
the decimal point moves to the right
while the digits move to the left.
25.9 x 10 = . 2 5 9
Decimal moves 1 place to the right because there is 1 zero .
Digits move 1 place to the left because there is 1 zero 2 5 9

3. Calculate 34.2 x 10
First, look at the number in the place value table... .
Now, where does 34.2 belong in this table? 3 4 2 .

4. . . 3 4 2 . 124 x 10 Multiplying by 10 means every digit must
move left by 1 column because there is 1 zero . . 3 4 2
Decimal moves one place to the right
because there is 1 zero
while the digits move to the left. .
So now we know that 34.2 x 10 =
342

5. Calculate x 100
First, look at the number in the place value table... .
Now, where does belong in this table? 3 6 . 9 4

6. . . 3 6 9 4 . 36.94 x 100 Multiplying by 100 means every digit must
move left by 2 columns because there are 2 zeros . . 3 6 9 4 .
So now we know that x 100 =
3694

7. . 5 1 2 . 1 Calculate 12.105 x 100 First, draw a place value table...
Now, where does belong in this table? 5 1 2 . 1

8. . . 1 2 1 5 . 12.105 x 100 Multiplying by 100 means every digit must
move left by 2 columns because there are 2 zeros . . 1 2 1 5
1210.5 .
So now we know that x 100 =

9. Remember the rules…
What is the rule for multiplying a whole number by 10?
Write down the number and add a zero
What is the rule for multiplying a whole number by 100?
Write down the number and add two zeros
TO SUM IT UP – multiply and then add the zeros

10. Take a look… Calculate 30 X 40 Multiply 3 X 4 = 12
How many zeros in the question?
Two
30 X 40 = 1200

11. Here we go again… Calculate 40 X 500 Multiply 4 by 5 = 20
How many zeros in the question?
Three
40 X 500 = 20,000

12. Your Turn!
x 10 =
200 x 70=
160 x 100 =
3.2 x 1000 =
12 x 10 =
136 x 10 =
2.2 x 10 =
14.6 x 10 =
120
464.41
14000
1360
16000 22
3200
146

13. Multiplying by 0.1 and 0.01 What is 4 × 0.1?
We can think of this as 4 sets of 0.1 or
We can also think of this as 4 × 1 10
which is the same as 4 ÷ 10
Therefore,
4 × 0.1 = 0.4
Multiplying by 0.1
Dividing by 10
is the same as
**TRICK- 0.1 move the invisible decimal 1 place to the left**

14. Multiplying by 0.1 and 0.01 What is 3 × 0.01?
We can think of this as 3 lots of 0.01 or 1
100
We can also think of this as 3 ×
which is equivalent to 3 ÷ 100
Therefore,
3 × 0.01 = 0.03
Multiplying by 0.01
Dividing by 100
is the same as
**TRICK move the invisible decimal 2 place to the left**

15. Multiplying by 0.1 and 0.01 4 × 0.1 = 0.4 Multiplying by 0.1
Dividing by 10
is the same as
**TRICK- 0.1 move the invisible decimal 1 place to the left**
3 × 0.01 = 0.03
Multiplying by 0.01
Dividing by 100
is the same as
**TRICK move the invisible decimal 2 place to the left**