rounding (significant figures)
TRANSCRIPT
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If you read in the Saturday sports section of the paper that the attendance at a football match was exactly 43,786 and a friend asked you about the attendance at school on Monday, you would probably say about 44,000. In this case you are giving an approximate answer to 2 S.f.
Significant Figures
It is often necessary/convenient/sensible to give approximations to real life situations or as answers to certain calculations.
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4 . 3 3 2 5
Significant Figures (Rounding)
Numbers can be rounded to 1,2, 3 or more significant figures. We count the number of figures from the first non-zero digit.
Rounding to 1 s.f
5 or bigger ?
4
5. 7 4 2 5
5 or bigger ?
6
0. 0 4 2 5
5 or bigger ?
0.04
No Yes No
First non-zero
digit.
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Rounding to 1 s.f
0 . 0 7 6
5 or bigger ?
0.08
0. 0 0 1 5
5 or bigger ?
0.002
Yes Yes
First non-zero
digit.
First non-zero
digit.
Significant Figures (Rounding)
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1 . 4 7 2 9
5 or bigger ?
1.5
0. 0 5 3 5
5 or bigger ?
0.054
Yes Yes
First non-zero
digit.
Significant Figures (Rounding)
Rounding to 2 s.f
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6 . 0 7 2 9
5 or bigger ?
6.1
0. 0 0 0 5 6 3
5 or bigger ?
0.00056
Yes No
First non-zero
digit.
Significant Figures (Rounding)
Rounding to 2 s.f
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2 . 0 7 5 9
5 or bigger ?
2.08
0. 0 2 0 4 6 3
5 or bigger ?
0.0205
Yes Yes
First non-zero
digit.
Significant Figures (Rounding)
Rounding to 3 s.f
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2 . 0 7 5 1
5 or bigger ?
2.075
0. 0 1 0 2 3 8 3
5 or bigger ?
0.01024
No Yes
First non-zero
digit.
Significant Figures (Rounding)
Rounding to 4 s.f
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Significant Figures (Rounding)
When we approximate whole numbers we may need to insert zeros as required in order to maintain the size of the number.
Rounding whole numbers to 1 s.f
1 4 7 2
5 or bigger ?
1 000
No
2 2 7 2 8
5 or bigger ?
20 000
No
4 8 8 1 3 5
5 or bigger ?
500 000
Yes
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Significant Figures (Rounding)
When we approximate whole numbers we may need to insert zeros as required in order to maintain the size of the number
Rounding whole numbers to 1 s.f
2 4 1
5 or bigger ?
200
No
5 8 7
5 or bigger ?
600
Yes
7 5
5 or bigger ?
80
Yes
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Significant Figures (Rounding)
When we approximate whole numbers we may need to insert zeros as required in order to maintain the size of the number
Rounding whole numbers to 2 s.f
1 4 7 2
5 or bigger ?
1 500
Yes
4 2 7 2 8
5 or bigger ?
43 000
Yes
2 0 4 4 7 8
5 or bigger ?
200 000
No
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Significant Figures (Rounding)
When we approximate whole numbers we may need to insert zeros as required in order to maintain the size of the number
Rounding whole numbers to 2 s.f
2 4 3
5 or bigger ?
240
No
2 8 7
5 or bigger ?
290
Yes
7 5 6
5 or bigger ?
760
Yes
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Significant Figures (Rounding)
When we approximate whole numbers we may need to insert zeros as required in order to maintain the size of the number
Rounding whole numbers to 3 s.f
5 4 7 2
5 or bigger ?
5 470
No
8 3 7 9 8
5 or bigger ?
83 800
Yes
9 7 4 9 7 8
5 or bigger ?
975 000
Yes
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Significant Figures (Rounding)
When we approximate whole numbers we may need to insert zeros as required in order to maintain the size of the number
Rounding whole numbers to 4 s.f
3 4 7 2 1
5 or bigger ?
34 720
No
1 3 7 9 8
5 or bigger ?
13 800
Yes
6 2 4 7 7 8
5 or bigger ?
624 800
Yes
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The following number could be the population of a country at a particular instant in time.Write this number to 1, 2, 3, 4, 5, 6 and 7 significant figures.
56 345 678
60 000 000 56 000 000 56 300 000
56 350 000 56 346 000 56 345 700
56 345 680