1. POWERS OF TEN

2. Which Numbers are The Powers of 10?
are the numbers produced when, starting with one (1), and repeatedly collect them into groups of 10.
1, 10, 100 etc
0.1, 0.01, etc

3. Number Ten (10) Number Ten (10) is a collection of ten Ones.
  10 = 10 x 1

4. Number One Hundred (100)
One Hundred (100) is a collection of ten Tens.
100 = 10 x 10

5. Number One Thousand (1 000)
One Thousand (1000) is a collection of ten One Hundreds
10 x 100   

6. The Whole POWERS OF TEN One 1 Ten 10 One hundred 100 One thousand
The Powers of 10
The Whole POWERS OF TEN
   One 1
   Ten 10
   One hundred
100
   One thousand
1,000
   Ten thousand
10,000
   One hundred thousand
100,000
   One million
1,000,000
   Ten million
10,000,000
   One hundred million
100,000,000
   One billion
1,000,000,000
   Ten billion
10,000,000,000
   One hundred billion
100,000,000,000

7. The Decimal POWERS OF TEN
   One Tenth
0.1
1/10
   One Hundredth
0.01
1/100
 One Thousandth
0.001
1/1000
  One Ten Thousandth
0.0001
1/10 000
   One Hundred Thousandth 1/
  One Millionth 1/

8. How To Multiply a Number By a Whole Power of 10?
Add a place for as many zeroes as appear in the power
The decimal moves as many places to the RIGHT as there are zeroes
Remember multiplying a whole number by a whole number means the answer should be bigger!
89 x 10 =89. x 10 = 890.
Decimal moves to the right one place

9. How To Multiply a Number By a Whole Power of 10?
Examples
36 × 10 = Add on one 0. (1 place)
36 x 100 = Add on two 0's. (2 places)
36 x 1000 = Add on three 0's.
(3 places)

10. How To Multiply a Number By a Decimal Power of 10?
Take a place away for each place past the decimal until a whole number is reached
e.g means move 2 places
0.01 moves 2 places to the right to get 1
** Remember multiplying a decimal number by a whole number means the answer should be getting smaller!

11. How To Multiply a Number By a Decimal Power of 10?
Examples
3400 x = = = 3.4
3400 x 0.01 = = = 34
3400 x 0.1 = = = 340
The decimal in the whole number moves as many places to the LEFT

12. How To Multiply a Number By a Decimal Power of 10?
Or move the decimal to the LEFT for each zero in the denominator
e.g is equal to 1/ and there are two zeroes in the denominator
= 1/ zero = 1 place to the LEFT
= 1/ zeroes = 2 places to the LEFT
= 1/ zeroes = 3 places to the LEFT
= 1/ zeroes = 4 places to the LEFT

13. How To Multiply a Number By a Decimal Power of 10?
Examples
3400 x = 3400 x 1/1000= = 3.4 (3 places)
3400 x 0.01 = x 1/100 = = (2 places)
3400 x = 3400 x 1/10 = = 340 (1 place)
The decimal in the whole number moves as many places to the LEFT

14. PRACTICE Find the product. Write the rule for multiplying by 100.
a) 100 x 350
b) 100 x 35
c) 100 x 3.5
d) 100 x 0.35
e) 679 x 100
f) 67.9 x 100
g) 6.79 x100
h) x 100

15. PRACTICE Find the product. Write the rule for multiplying by 100.
a) 100 x =
b) 100 x = 3 500
c) 100 x = 350
d) 100 x = 35
e) 679 x =
f) 67.9 x = 6 790
g) 6.79 x = 679
h) x = 67.9
Rule: ??

16. PRACTICE Find the product. Write the rule for multiplying by 100.
a) 100 x =
b) 100 x = 3 500
c) 100 x = 350
d) 100 x = 35
e) 679 x =
f) 67.9 x = 6 790
g) 6.79 x = 679
h) x = 67.9
Rule: When Multiplying by 100 move decimal 2 places to the Right

17. PRACTICE Multiply the following a) 234 x 100 b) 0.01 x 29 c) 300 x 0.1
d) x1000
e) 10 x 4.3
f) x 600
g) 0.1 x 56.3
h) x 8300

18. PRACTICE Multiply the following a) 234 x 100 = 23 400
b) x = 0.29
c) 300 x = 30
d) x =
e) 10 x = 43
f) x = 0.6
g) 0.1 x = 5.63
h) x =

19. How To Divide a Number By a Whole Power of 10?
take away a place for as many zeroes as appear in the power
The decimal moves as many places to the LEFT as there are zeroes
Remember dividing a whole number by a whole number means the answer should be smaller!
89 ÷ 10 =89. ÷ 10 = 8.9
Decimal moves to the left one place

20. How To Divide a Number By a Whole Power of 10?
Examples
36 ÷ 10 = Take away 1 place (one 0)
36 / 100 = Take away 2 place (two 0)
36 ÷ 1000 = Take away 3 place (three 0)

21. HOW TO DIVIDE A WHOLE NUMBER BY A DECIMAL POWER OF TEN
Add a place for each place past the decimal until a whole number is reached
e.g means move 2 places
0.01 moves 2 places to the right to get 1
** Remember dividing a whole number by a decimal means the answer should be getting bigger!

22. HOW TO DIVIDE A WHOLE NUMBER BY A DECIMAL POWER OF TEN
Examples
3400 ÷ =
3400 / 0.01 =
3400 ÷ 0.1 =
The decimal in the whole number moves as many places to the RIGHT

23. HOW TO DIVIDE A WHOLE NUMBER BY A DECIMAL POWER OF TEN
Or move the decimal to the RIGHT for each zero in the denominator
e.g is equal to 1/ and there are two zeroes in the denominator
= 1/ zero = 1 place to the RIGHT
= 1/ zero = 2 place to the RIGHT
= 1/ zeroes = 3 place to the RIGHT
= 1/ zeroes = 4 place to the RIGHT

24. HOW TO DIVIDE A WHOLE NUMBER BY A DECIMAL POWER OF TEN
Examples
3400 / = 3400 ÷ 1/1000= (3 places)
3400 ÷ 0.01 = ÷ 1/100 = (2 places)
3400 ÷ = 3400 ÷ 1/10 = (1 place)
The decimal in the whole number moves as many places to the RIGHT

25. PRACTICE Divide a) 365 ÷ 10 b) 365 ÷ 100 c) 365 ÷ 1000 d) 8970 ÷ 0.1
f) 8970 ÷ 0.001

26. PRACTICE Divide 365 ÷ 10 = 36.5 365 ÷ 100 = 3.65 365÷ 1000 = 0.365
365÷ = 0.365
8970 ÷ 0.1 =
8970 ÷ 0.01 =
8970 ÷ =