Chapter 1, Problem 2P

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?

To determine

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.

To determine

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.

To determine

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.

To determine

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.

To determine

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.

To determine

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.

To determine

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.