SIGNIFICANT FIGURES DEFINITION.
-Significant figures are all non-zero digits, example 7436, the 7, 4, 3 and 6 are non-zero digits hence are significant figures.
-A zero (or zero) between non-zero digits is (are) significant figures. Example 7046 and 4003, the zero between non-zero digits is (are) Significant figures.
Example
5007=5000(to 1 significant figure)
Explanation.
The first significant figure in 5007 is 5 and the next number to the right of 5 is 0 which is below five, hence the 5 remains the same and we obtain a new number 5000.
5007=5000(to 2 significant figures)
Explanation.
The second significant figure 5007 is 0 and the next number to the right of 0 is 0 which is below five, hence the 0 remains the same and we obtain a new number 5000.
5007=5010(to 3 significant figures)
Explanation.
The third significant figure in 5007 is 0 and the next number to the right of 0 is 7 which is above five, hence we round up 0 to 1 and we obtain a new number 5010.
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5347=5000(to 1 significant figure)
Explanation.
The first significant figure in 5347 is 5 and the next number to the right of 5 is 3 which is below five, hence the 5 remains and we obtain a new number 5000.
5347=5300(to 2 significant figures)
Explanation.
The second significant figure in 5347 is 3 and the next number to the right of 3 is 4 which is below five, hence the 3 remains and we obtain a new number 5300.
5347=5350(to 3 significant figures)
Explanation.
The third significant figure in 5347 is 4 and the next number to the right of 4 is 7 which is above five, hence we round up 4 to 5 and obtain a new number 5350.
Example
Express 4033 correct to.
a) 1 significant figure.
ANS: To 1 significant figure (=4000)
b) 2 significant figures
ANS: To 2 significant figures (=4000)
c) 3 significant figures
ANS: To 3 significant figures (=4030)
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Express 789 correct to
a) 1 significant figure.
b) 2 significant figures.
Significant figures for decimal numbers.
-In a decimal, zeros before the first non-zero digit are not significant.
Example: 0.00503
The first three zeros on the left side are not significant figures.
Exercise:
1. Round the following numbers to one significant figure.
a) 0.0672
ANS: To one significant figure (=0.0700)
Explanation.
The first significant figure in 0.0672 is 6 and the next number to the right of 6 is 7 which is above 5, hence we round up 6 to 7 and obtain a new number 0.0700.
b) 0.349
ANS: To one significant figure (=0.300)
Explanation.
The first significant figure in 0.349 is 3 and the next number to the right of 3 is 4 which is below 5, hence the 3 remains the same and obtain a new number 0.300.
c) 0.00055
ANS: To one significant figure (=0.0006)
Explanation.
The first significant figure in 0.00055 is 5 and the next number to the right of 5 is 5 which is equal to 5, hence we round up 5 to 6 and obtain a new number 0.00060
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d) 0.0197
e) 0.000798
2. Round the following numbers to two significant figures.
a) 674.81
ANS: To two significant figure (=670.00)
Explanation.
The second significant figure in 674.81 is 7 and the next number to the right of 7 is 4 which is below 5, hence the 7 remains the same and we obtain a new number 670.00
b) 974.008
ANS: To two significant figures (=970.00)
Explanation.
The second significant figure in 974.008 is 7 and the next number to the right of 7 is 4 which is below 5, hence the 7 remains the same and we obtain a new number 970.00
c) 0.003753
ANS: To two significant figures (=0.0038)
Explanation.
The second significant figure in 0.003753 is 7 and the next number to the right of 7 is 5 which is equal to 5, hence we round up 7 to 8 and obtain a new number 0.0038.
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d) 0.0001792
e) 0.5635
3. Round the following to three significant figures.
a) 80.569
ANS: To three significant figures (=80.600)
Explanation.
The third significant figure in 80.569 is 5 and the next number to the right of 5 is 6 which is above 5, hence we round up 5 to 6 and obtain a new number 80.600
b) 0.08521
ANS: To three significant figures (=0.08520)
Explanation.
The third significant figure in 0.08521 is 2 and the next number to the right of 2 is 1 which is below 5, hence the 2 remains the same and we obtain a new number 0.08520
c) 0.00041769
ANS: To three significant figures (=0.00041800)
Explanation.
The third significant figure in 0.00041769 is 7 and the next number to the right of 7 is 6 which is above 5, hence we round up 7 to 8 and obtain a new number 0.00041800.
Try these
d) 146.83
e) 0.10653 4.
4.The density of Hydrogen gas is 0.0899kg/m^3. Round this density to one significant figure.
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