Transcript Significant figures

SIGNIFICANT FIGURES AND
DECIMAL PLACES
Decimal places
It is often useful to give an answer to a number of decimal places.
If you are asked to round a number to 2 decimal places you must have
exactly 2 digits after the decimal point.
The following rules are used:
1. Count along the digits to the required number of decimal places.
2. Look at the next digit
• If it is less than 5, leave the digit before it as it is.
• If it is 5 or more, you must round up the digit before it.
Examples
1 Write 5.3472 correct to 2 decimal places.
5.3472
5.3472 = 5.35 to 2 d.p.
the next digit is 7 so you must round up
Examples
2 Write 36.4319 correct to 2 decimal places.
36.4319
36.4319 = 36.43 to 2 d.p.
the next digit is 1 so the digit
before it will not change
Examples
3 Write 0.0088 correct to 2 decimal places.
0.0088
0.0088 = 0.01 to 2 d.p.
the next digit is 8 so you must round up
Examples
4 Write 126.2043 correct to 2 decimal places.
126.2043
126.2043 = 126.20 to 2 d.p.
the next digit is 4 so the digit
before it will not change
note: you must keep the 0 in your answer
Examples
5 Write 27.998 correct to 2 decimal places.
27.998
27.998 = 28.00 to 2 d.p.
the next digit is 8 so you must round up
Examples
6 Write 49.3254 correct to 3 decimal places.
49.3254
49.3254 = 49.325 to 3 d.p.
the next digit is 4 so the digit
before it will not change
Examples
7 Write 7.8798 correct to 3 decimal places.
7.8798
7.8798 = 7.880 to 3 d.p.
the next digit is 8 so you must round up
Significant figures
You may also be asked to round to a number of significant figures.
To round a number to a given number of significant figures use the
following rules:
1. Count along the digits to the required number of significant figures.
(The most significant figure is the first non-zero figure.)
2. Look at the next digit
• If it is less than 5, leave the digit before it as it is.
• If it is 5 or more, you must round up the digit before it.
Examples
1 Write 53872 correct to 2 significant figures.
53872
53872 = 54000 to 2 s.f.
the next digit is 8 so you must round up
Examples
2 Write 76408 correct to 1 significant figure.
76408
76408 = 80000 to 1 s.f.
the next digit is 6 so the digit
before it will not change
Examples
3 Write 6.439 correct to 3 significant figures.
6.439
6.439 = 6.44 to 3 s.f.
the next digit is 9 so you must round up
Examples
4 Write 0.00342 correct to 2 significant figures.
0.00342
0.00342 = 0.0034 to 2 s.f.
the next digit is 2 so the digit
before it will not change
Examples
5 Write 0.00899 correct to 2 significant figures.
0.00899
0.00899 = 0.0090 to 2 s.f.
the next digit is 9 so you must round up
Estimating
It is important that you know how to check if your answer to a calculation
is a sensible answer.
To estimate the answer to a calculation use the
following steps:
1. Round each of the numbers to 1 significant figure.
2. Do the calculation using your rounded numbers.
Examples
1 Estimate the answer to 5.78  2.14
5.78  6
2.14  2
5.78  2.14  6  2  12
2 Estimate the answer to 28.217  2.97
28.217  30
2.97  3
28.217  2.97  30  3  10
Examples
3 Estimate the answer to 42.8  4.11
3.22  5.96
42.8  40
4.11 4
3.22  3
5.96  6
42.8  4.11 40  4

3.22  5.96 3  6

36
18
2
Examples
4 Estimate the answer to 389  813.7
(40.6)2
389  400
813.7  800
10 20
389  813.7 400  800

2
40  40
(40.6)
 200
40.6  40