Multiplying and Dividing by 10, 100, 1000 etc. Because our ... - Unitec

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Multiplying and Dividing by 10, 100, 1000 etc.
Because our number system is based on 10 we have short cut ways of multiplying and
dividing by 10, 100, 1000 etc. We use this to convert metric units, calculate with
percentages etc.
Multiplying by 10, 100, or 1000
1. If you are multiplying by 10, 100, 1000 etc move the decimal point 1, 2, 3 etc.
places to the right.
Hint: The number of places you move the decimal point matches the number of
0s on the number you are multiplying by.
Examples:
6.435 x 10 = 64.35, 6.435 x 100 = 643.5, 6.435 x 1000 = 6435. = 6435
Note: If the decimal point moves out of the number (as in the last example) then it
is not written.
2. If there are not enough numbers to move over then add 0s until there are.
Examples: 6.4 x 10 = 64 6.4 x 100 = 640 6.4 x 1000 = 6400
Hint: If you are left with 0s at the beginning of the number they are left out
Examples: 0.6 x 10 = (06.) = 6 0.006 x 10 = (00.06) = 0.06
Exercise 1
1. 4.15 x 10 2. 6.81 x 10 3. 31.4 x 10 4. 0.071 x 10
5. 33.6 x 10 6. 0.09 x 10 7. 16.8 x 10 8. 0.04 x 10
9. 1.63 x 10 10. 0.004 x 10 11. 24 x 10 12. 240 x 10
Unitec:\ H:\Te Puna Ako Learning Centre\Maths and Statistics Resources\updated\Multiplying and Dividing by 10,100,1000 etc..doc

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Exercise 2
1. 14.41 x 100 2. 1.71 x 100 3. 0.042 x 100 4. 0.61 x 100
5. 11.4 x 100 6. 8.3 x 100 7. 9.7 x 100 8. 0.41 x 100
9. 0.041 x 100 10. 4.66 x 100 11. 24 x 100 12. 240 x 100
Exercise 3 – Multiply these numbers by 1000
1. 0.41 2. 6.81 3. 31.4 4. 0.071 5. 33.6
6. 0.09 7. 16.8 8. 0.04 9. 1.63 10. 0.004
11. 24 12. 240
(Answers at end)
Dividing by 10, 100, 1000
1. If you are dividing by 10, 100, 1000 etc. and the number has a decimal point in it
move the decimal point 1, 2 3 etc. places to the left.
Hint: The number of places you move the decimal point matches the number of
0s on the number you are dividing by.
Hint: If there are not enough numbers to move over then add 0s until there are.
Examples:
32.4 10 = 3.24 2.4 10 = 0.24 0.4 10 = 0.04
132.4 100 = 1.324 32.4 100 = 0.324 2.4 100 = 0.024
132.4 ÷ 1000 = 0.1324 2.4 ÷1000 = 0.0024
Note: Usually a zero is written before the decimal point if a number starts with the
decimal point – 0.6 rather than .6
2. If there is no decimal point in the number it is a whole number and the decimal
point can be written at the end of the number. For example 6 is 6. or 256 is
256.
Unitec:\ H:\Te Puna Ako Learning Centre\Maths and Statistics Resources\updated\Multiplying and Dividing by 10,100,1000 etc..doc

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Examples:
6 10 = 0.6 60 10 = 6 6 100 = 0.06
60 100 = 0.6 6 ÷ 1000 = 0.006
Exercise 4:
1. 33 10 2. 19.63 10 3. 1.9 10 4. 0.88 10
5. 0.09 10 6. 0.41 10 7. 9.8 10 8. 98 10
9. 0.18 10 10. 0.07 10
Exercise 5
1. 17.4 100 2. 8.88 100 3. 99 100 4. 934 100
5. 0.44 100 6. 0.02 100 7. 0.41 100 8. 3.8 100
9. 33 100 10. 185 100
Exercise 6 – Divide these numbers by 1000
1. 33 2. 19.63 3. 1.9 4. 880 5. 9362
6. 123.4 7. 118 8. 698 9. 0.18 10. 0.07
(Answers at end)
Caution: If you are doing okay do not go any further. If, however, you have a lot of
unnecessary 0s in your answers read on!
When do we leave zeroes in a number and when can we leave them out ?
If the zeroes are at the beginning of a number before any other digits and the decimal
point we can leave them out. (Usually one zero is written before the decimal point if a
number starts with the decimal point – 0.6 rather than .6 )
Example: 07 = 7, 0060 = 60 but 0.006 must keep the zeroes because they are after
the decimal point
Unitec:\ H:\Te Puna Ako Learning Centre\Maths and Statistics Resources\updated\Multiplying and Dividing by 10,100,1000 etc..doc

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If the zeroes are at the end of a number after any other digits and the decimal point we
can leave them out.
Example: 6.40000 = 6.4, 6.40400 = 6.404
Other than that leave them there!!
Exercise 7: Re-write the numbers without the unnecessary zeroes
1. 3.090 2. 0.00600 3. 1.071010 4. 0.09020 5. 0.700
6. 7.070 7. 4.303 8. 0.009000 9. 3.0010 10. 6.010
11. 08.3 12. 8000 13. 71.610 14. 07100 15. 09.20
16. 0.06 17. 0071.03 18. 1.03 19. 07.00170 20. 6.070
Answers
Exercise 1
1. 41.5 2. 68.1 3. 314 4. 0.71 5. 336 6. 0.9 7. 168
8. 0.4 9. 16.3 10. 0.04 11. 240 12. 2400
Exercise 2
1. 1441 2. 171 3. 4.2 4. 61 5. 1140 6. 830 7. 970
8. 41 9. 4.1 10. 466 11. 2400 12. 24000
Exercise 3
1. 410 2. 6810 3. 31400 4. 71 5. 33600 6. 90 7. 16800
8. 40 9. 1630 10. 4 11. 24000 12. 240000
Exercise 4:
1. 3.3 2. 1.963 3. 0.19 4. 0.088 5. 0.009 6. 0.041 7. 0.98
8. 9.8 9. 0.018 10. 0.007
Exercise 5
1. 0.174 2. 0.0888 3. 0.99 4. 9.34 5. 0.0044 6. 0.0002 7. 0.0041
8. 0.038 9. 0.33 10. 1.85
Exercise 6
1. 0.033 2. 0.01963 3. 0.0019 4. 0.88 5. 9.362 6. 0.1234 7. 0.118
8. 0.698 9. 0.00018 10. 0.00007
Exercise 7
1. 3.09 2. 0.006 3. 1.07101 4. 0.0902 5. 0.7 6. 7.07 7. 4.303
8. 0.009 9. 3.001 10. 6.01 11. 8.3 12. 8000 13. 71.61 14. 7100
15. 9.2 16. 0.06 17. 71.03 18. 1.03 19. 7.0017 20. 6.07
Unitec:\ H:\Te Puna Ako Learning Centre\Maths and Statistics Resources\updated\Multiplying and Dividing by 10,100,1000 etc..doc