
Concept explainers
How many significant figures do each of the following numbers have: (a) 214, (b) 81.60, (c) 7.03, (d) 0.03, (e) 0.0086, (f)3236, and (g) 8700?
(a)

Find thenumber of significant figures of the number 214.
Answer to Problem 2P
Solution:
Number of significant figures is 3.
Explanation of Solution
214 is a number and we have to find its significant number by following certain rules given below.
Rules for determining the number significant figures -
- All non-zero digits are significant.
- All zeroes between non-zero digits are significant.
- All zeroes to the right of the last non-zero digit are not significant in number without a decimal point.
- All zeroes to the right of a decimal and to the left of a non-zero digit are not significant.
- All zeroes to the right of the decimal and to the right of a non-zero digit are significant.
- In addition and subtraction, we should retain the least decimal place among the value operated in the result.
- In multiplication and division, we should express the result with least number of significant figures as associated with the least precise number in operation.
Conclusion:
Here, the number of significant figures is 3 according to rule - All non-zero digits are significant.
(b)

Find the number of significant figures of the number 81.60
Answer to Problem 2P
Solution:
Number of significant figures is 4.
Explanation of Solution
81.60 is a number and we have to find its significant number by following certain rules given below.
Rules for determining the number significant figures -
- All non-zero digits are significant.
- All zeroes between non-zero digits are significant.
- All zeroes to the right of the last non-zero digit are not significant in number without a decimal point.
- All zeroes to the right of a decimal and to the left of a non-zero digit are not significant.
- All zeroes to the right of the decimal and to the right of a non-zero digit are significant.
- In addition and subtraction, we should retain the least decimal place among the value operated in the result.
- In multiplication and division, we should express the result with least number of significant figures as associated with the least precise number in operation.
Conclusion:
Here, the number of significant figures is 4 according to rule - All zeroes to the right of the decimal and to the right of a non-zero digit are significant.
(c)

Find the number of significant figures of the number 7.03
Answer to Problem 2P
Solution:
Number of significant figures is 3.
Explanation of Solution
7.03 is a number and we have to find its significant number by following certain rules given below.
Rules for determining the number significant figures -
- All non-zero digits are significant.
- All zeroes between non-zero digits are significant.
- All zeroes to the right of the last non-zero digit are not significant in number without a decimal point.
- All zeroes to the right of a decimal and to the left of a non-zero digit are not significant.
- All zeroes to the right of the decimal and to the right of a non-zero digit are significant.
- In addition and subtraction, we should retain the least decimal place among the value operated in the result.
- In multiplication and division, we should express the result with least number of significant figures as associated with the least precise number in operation.
Here, the number of significant figures is 3 according to rule - Zeroes between non-zero digits are always significant.
(d)

Find the number of significant figures of the number 0.03
Answer to Problem 2P
Solution:
Number of significant figures is 1
Explanation of Solution
0.03 is a number and we have to find its number of significant figures by following certain rules given below.
Rules for determining the number of significant figures -
- All non-zero digits are significant.
- All zeroes between non-zero digits are significant.
- All zeroes to the right of the last non-zero digit are not significant in number without a decimal point.
- All zeroes to the right of a decimal and to the left of a non-zero digit are not significant.
- All zeroes to the right of the decimal and to the right of a non-zero digit are significant.
- In addition and subtraction, we should retain the least decimal place among the value operated in the result.
- In multiplication and division, we should express the result with least number of significant figures as associated with the least precise number in operation.
Here, the number of significant figures is 1 according to rule - Zeroes at the beginning of the number are non-significant.
(e)

Find the number of significant figures of the number 0.0086
Answer to Problem 2P
Solution:
Number of significant figures is 2.
Explanation of Solution
0.0086 is a number and we have to find its number of significant figures by following certain rules given below.
Rules for determining the number of significant figures -
- All non-zero digits are significant.
- All zeroes between non-zero digits are significant.
- All zeroes to the right of the last non-zero digit are not significant in number without a decimal point.
- All zeroes to the right of a decimal and to the left of a non-zero digit are not significant.
- All zeroes to the right of the decimal and to the right of a non-zero digit are significant.
- In addition and subtraction, we should retain the least decimal place among the value operated in the result.
- In multiplication and division, we should express the result with least number of significant figures as associated with the least precise number in operation.
Here, the number of significant figures is 2 according to rule - Zeroes at the beginning of the number are non-significant.
(f)

Find the number of significant figures of the number 3236
Answer to Problem 2P
Solution:
Number of significant figures is 4.
Explanation of Solution
3236 is a number and we have to find its number of significant figures by following certain rules given below.
Rules for determining the number significant figures -
- All non-zero digits are significant.
- All zeroes between non-zero digits are significant.
- All zeroes to the right of the last non-zero digit are not significant in number without a decimal point.
- All zeroes to the right of a decimal and to the left of a non-zero digit are not significant.
- All zeroes to the right of the decimal and to the right of a non-zero digit are significant.
- In addition and subtraction, we should retain the least decimal place among the value operated in the result.
- In multiplication and division, we should express the result with least number of significant figures as associated with the least precise number in operation.
Here, the number of significant figures is 4 according to rule - All non-zero numbers are significant.
(g)

Answer to Problem 2P
Solution:
No. of significant figures is 2.
Explanation of Solution
8700 is a number and we have to find its number of significant figures by following certain rules given below.
Rules for determining the number significant figures -
- All non-zero digits are significant.
- All zeroes between non-zero digits are significant.
- All zeroes to the right of the last non-zero digit are not significant in number without a decimal point.
- All zeroes to the right of a decimal and to the left of a non-zero digit are not significant.
- All zeroes to the right of the decimal and to the right of a non-zero digit are significant.
- In addition and subtraction, we should retain the least decimal place among the value operated in the result.
- In multiplication and division, we should express the result with least number of significant figures as associated with the least precise number in operation.
Here, the number of significant figures is 2 according to rule - All zeroes to the right of the last non-zero digit are not significant in number without a decimal point.
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