This document provides instruction on multiplying and dividing by powers of ten. It explains that for multiplication, the decimal point moves right for whole number powers of ten and left for decimal powers of ten. For division, the decimal point moves left for whole number powers of ten and right for decimal powers of ten. Examples are provided to demonstrate these rules. Students are asked to practice these concepts by solving problems mentally in their notebooks.

1. 4.5 Multiplying And
Dividing by Powers
of Ten
October 21, 2010

2. What happens when you multiply
by powers of ten?
Fill in the blanks below (in your
notebook).
Whole Number Powers of Ten Decimal Powers of Ten
10 x 8.3 = _____ 0.1 x 8.3 = _____
100 x 8.3 = _____ 0.01 x 8.3 = _____
1000 x 8.3 = _____ 0.001 x 8.3 = _____
10,000 x 8.3 = _____ 0.0001 x 8.3 = _____

3. What happens when you multiply
by powers of ten?
Check your answers (in your
notebook).
Whole Number Powers of Ten Decimal Powers of Ten
10 x 8.3 = 83 0.1 x 8.3 = 0.83
100 x 8.3 = 830 0.01 x 8.3 = 0.083
1000 x 8.3 = 8,300 0.001 x 8.3 = 0.0083
10000 x 8.3 = 83,000 .0001 x 8.3 = .00083

4. Multiplying by
Powers of Ten

5. Multiplying by
Powers of Ten
***Copy this in your notebook:

6. Multiplying by
Powers of Ten
***Copy this in your notebook:
Multiplying by whole number powers of 10: Move the
decimal point one place to the right for each zero in
the whole number power 10.

7. Multiplying by
Powers of Ten
***Copy this in your notebook:
Multiplying by whole number powers of 10: Move the
decimal point one place to the right for each zero in
the whole number power 10.
Numbers 3.995 x 100 = 3.99.5

8. Multiplying by
Powers of Ten

9. Multiplying by
Powers of Ten
***Copy this in your notebook:

10. Multiplying by
Powers of Ten
***Copy this in your notebook:
Multiplying by decimal number powers of 10: Move
the decimal point one place to the left for each zero in
the whole number power 10.

11. Multiplying by
Powers of Ten
***Copy this in your notebook:
Multiplying by decimal number powers of 10: Move
the decimal point one place to the left for each zero in
the whole number power 10.
Numbers 399.5 x 0.001 = 399.5

12. Try these on your own (in
your notebook)
Multiply decimals using mental maths:
0.05 x 1000 =
95.38 x 0.0001

13. Check your answer (in
your notebook)

14. Check your answer (in
your notebook)
Multiply decimals using mental maths:

15. Check your answer (in
your notebook)
Multiply decimals using mental maths:
0.05 x 1000 = 50

16. Check your answer (in
your notebook)
Multiply decimals using mental maths:
0.05 x 1000 = 50
Move the decimal 3 places to the right.

17. Check your answer (in
your notebook)
Multiply decimals using mental maths:
0.05 x 1000 = 50
Move the decimal 3 places to the right.
95.38 x 0.0001 = 0.0009538

18. Check your answer (in
your notebook)
Multiply decimals using mental maths:
0.05 x 1000 = 50
Move the decimal 3 places to the right.
95.38 x 0.0001 = 0.0009538
Move the decimal 4 places to the left.

19. Dividing by Powers
of Ten

20. Dividing by Powers
of Ten
*** Copy this in your notebook.

21. Dividing by Powers
of Ten
*** Copy this in your notebook.
Dividing by Whole Number Powers of 10: Move the
decimal point one place to the left for each zero in the
whole number power of 10.

22. Dividing by Powers
of Ten
*** Copy this in your notebook.
Dividing by Whole Number Powers of 10: Move the
decimal point one place to the left for each zero in the
whole number power of 10.
35 ÷ 100 = 0.35. = 0.35

23. Dividing by Powers
of Ten

24. Dividing by Powers
of Ten
*** Copy this in your notebook.

25. Dividing by Powers
of Ten
*** Copy this in your notebook.
Dividing by Decimal Number Powers of 10: Move the
decimal point one place to the right for each zero in
the whole number power of 10.

26. Dividing by Powers
of Ten
*** Copy this in your notebook.
Dividing by Decimal Number Powers of 10: Move the
decimal point one place to the right for each zero in
the whole number power of 10.
35 ÷ 0.001 = 35.00 = 3,500

27. Divide Decimals Using Mental
Math (Now you try: in your
notebook)
• 508.3 ÷ 10
• 508.3 ÷ 0.01

28. Divide Decimals Using Mental
Math (Now you try: in your
notebook)
• 508.3 ÷ 10 = 50.83
Move 1 place to the left.
• 508.3 ÷ 0.01 = 50,830
Move 2 places to the right.

29. Try these (show these problems tomorrow with
your homework)
• 6.07 X 1000
• 153.6 X 0.01
• 42.6 ÷ 100
• 509 ÷ 1000
• 5 ÷ 0.1
• 3.2 ÷ 0.001

30. When you finish:
• You may begin your homework.