Chapter A, Problem 1E

(a)

To determine

The number of significant figures in 454g.

Answer to Problem 1E

Solution:

3

Explanation of Solution

Introduction:

Significant figures of a number are the number of digits with a meaningful contribution to the measurement. The use of significant figures is known to be reasonably reliable. The nonzero digits are always significant.

Explanation:

The significant figures for the quantity, 454 g, are 4, 5, and 4 as all are nonzero digits and nonzero digits are always significant. Thus, the quantity, 454 g, has three significant figures.

Conclusion:

The number of significant figures in the quantity, 454 g, is 3.

(b)

To determine

The number of significant figures in 2.2 N.

Answer to Problem 1E

Solution:

2

Explanation of Solution

Introduction:

Significant figures of a number are the number of digits with a meaningful contribution to the measurement. The use of significant figures is known to be reasonably reliable. The nonzero digits are always significant.

Explanation:

The significant figures for the quantity, 2.2 N, are 2 and 2 as both are nonzero digits and nonzero digits are always significant. Thus, the quantity, 2.2 N, has two significant figures.

Conclusion:

The number of significant figures in the quantity 2.2 N is 2.

(c)

To determine

The number of significant figures in 2.205 N.

Answer to Problem 1E

Solution:

4

Explanation of Solution

Introduction:

Significant figures of a number are the number of digits with a meaningful contribution to the measurement. The nonzero digits and the number 0between two nonzero digits are significant.

Explanation:

The significant figures for the quantity, 2.205 N, are 2, 2, 0, and 5. This is because the numbers 2, 2, and 5 are nonzero digits. Also, the digit 0 is between 2 and 5. Thus, all the digits 2, 2, 0, and 5 are significant and hence the quantity, 2.205 N, has four significant figures.

Conclusion:

The number of significant figures in the quantity 2.205 N is 4.

(d)

To determine

The number of significant figures in 0.3937 s.

Answer to Problem 1E

Solution:

4

Explanation of Solution

Introduction:

Significant figures of a number are the number of digits with a meaningful contribution to the measurement. The nonzero digits are always significant. And, the number zero, when used to fix the decimal point, can never be significant.

Explanation:

The significant figures for the quantity, 0.3937 s, are 3, 9, 3, and 7. This is because the numbers 3, 9, 3, and 7 are nonzero digits. Also, the digit 0 is used to fix the decimal point and is, thus, not significant. The number 0.3937 can be written in the exponential form as $3.937\times {10}^{-1}$. This number $3.937\times {10}^{-1}$ has four significant figures 3, 9, 3, and 7. Thus, the quantity, 0.3937 s, has four significant figures.

Conclusion:

The number of significant figures in the quantity, 0.3937 s, is 4.

(e)

To determine

The number of significant figures in 0.0353m.

Answer to Problem 1E

Solution:

3

Explanation of Solution

Introduction:

Significant figures of a number are the number of digits with a meaningful contribution to the measurement. The nonzero digits are always significant. Also, the number zero, when used to fix the decimal point, can never be significant.

Explanation:

The significant figures for the quantity, 0.0353 m, are 3, 5, and 3. This is because the numbers 3, 5, and 3 are all nonzero digits. Also, the digit 0 is used to fix the decimal point and is, thus, not significant. The number, 0.0353, can be written in the exponential form as $3.53\times {10}^{-2}$. This number, $3.53\times {10}^{-2}$, has three significant figures as 3, 5, and 3. Thus, the quantity, 0.0353 m, hasthree significant figures.

Conclusion:

The number of significant figures in the quantity, 0.0353 m, is 3.

(f)

To determine

The number of significant figures in 1.0080 hr.

Answer to Problem 1E

Solution:

5

Explanation of Solution

Introduction:

Significant figures of a number are the number of digits with a meaningful contribution to the measurement. The nonzero digits, the number zero between two significant figures, and the trailing zeros in the decimal portion are significant.

Explanation:

The significant figures for the quantity, $1.0080\text{ hr}$, are 1, 0, 0, 8, and 0. This is because the numbers 1 and8 are nonzero digits. Also, the zeros between 1 and 8 are significant as they are between two nonzero numbers. The number zero trailing the decimal portion, that is, 0 after 8 in the decimal portion is also significant. Thus, the quantity $1.0080\text{ hr}$ hasfive significant figures.

Conclusion:

The number of significant figures in the quantity, $1.0080\text{ hr}$, is 5.

(g)

To determine

The number of significant figures in 14.0 A.

Answer to Problem 1E

Solution:

3

Explanation of Solution

Introduction:

Significant figures of a number are the number of digits with a meaningful contribution to the measurement. The nonzero digits and the trailing zeros in the decimal portion are significant.

Explanation:

The significant figures for the quantity, 14.0 A, are 1, 4, and 0. This is because the numbers 1 and 4 are nonzero digits and the number 0trails the decimal portion. Thus, the quantity, 14.0 A, has three significant figures.

Conclusion:

The number of significant figures in the quantity, 14.0 A, is 3.

(h)

To determine

The number of significant figures in $9.3\times {10}^7\text{ km}$.

Answer to Problem 1E

Solution:

2

Explanation of Solution

Introduction:

Significant figures of a number are the number of digits with a meaningful contribution to the measurement. The nonzero digits are always significant. Also, the number 0thatis used to fix the decimal point can never be significant.

Explanation:

The significant figures for the quantity $9.3\times {10}^7\text{ km}$ are 9 and 3. This is because the numbers 9 and 3 are nonzero digits. Thus, the quantity $9.3\times {10}^7\text{ km}$ represents two significant figures.

Conclusion:

The number of significant figures in the quantity, $9.3\times {10}^7\text{ km}$, is 2.

(i)

To determine

The number of significant figures in $1.118\times {10}^{-3}\text{ V}$.

Answer to Problem 1E

Solution:

4

Explanation of Solution

Introduction:

Significant figures of a number are the number of digits with a meaningful contribution to the measurement. The nonzero digits are always significant. Also, the number 0thatis used to fix the decimal point can never be significant.

Explanation:

The significant figures for the quantity $1.118\times {10}^{-3}\text{ V}$ are 1, 1, 1, and 8. This is because the numbers 1, 1, 1, and 8 are all nonzero digits. Also, the digit 0 in the quantity, $1.118\times {10}^{-3}\text{ V}$ or $0.001118$, is used to fix the decimal point and is, thus, not significant. Thus, the quantity, $1.118\times {10}^{-3}\text{ V}$, represents four significant figures.

Conclusion:

The number of significant figures in the quantity, $1.118\times {10}^{-3}\text{ V}$, is 4.

(j)

To determine

The number of significant figures in $1030{\text{ kg/m}}^3$.

Answer to Problem 1E

Solution:

4

Explanation of Solution

Introduction:

Significant figures of a number are the number of digits with a meaningful contribution to the measurement. The nonzero digits and the number 0between two significant figures are significant.

Explanation:

The significant figures for the quantity, $1030{\text{ kg/m}}^3$, are 1, 0, 3, and 0. This is because the numbers 1 and 3 are nonzero digits, and 0 between 1 and 3 are significant as they are between two significant figures. Now, when the quantity, $1030{\text{ kg/m}}^3$, is measured to the nearest ${\text{kg/m}}^3$; the zero in the rightmost part is alsosignificant. Thus, the quantity $1030{\text{ kg/m}}^3$ represents four significant figures.

Conclusion:

The number of significant figures in the quantity, $1030{\text{ kg/m}}^3$, is 4.

(k)

To determine

The number of significant figures in $125,000\text{ N}$.

Answer to Problem 1E

Solution:

6

Explanation of Solution

Introduction:

Significant figures of a number are the number of digits with a meaningful contribution to the measurement. The nonzero digits are significant, and the trailing zeros in the decimal portion are significant.

Explanation:

The significant figures for the quantity, 125,000 N, are 1, 2, 5, and 0. This is because the numbers 1, 2, and 5 are all non-zero digits. Now, when the quantity, 125,000 N, is measured to the nearest newton, the zeros in the right portion after 5 are also significant. Thus, the quantity 125,000 Nrepresents six significant figures.

Conclusion:

The number of significant figures in the quantity, 125,000, is 6.