rounding (significant figures)
TRANSCRIPT
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.
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.
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)
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
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
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
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
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
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
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
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
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
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
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