Chapter PSS, Problem 20E

Interpretation Introduction

(a)

Interpretation:

The given nonsignificant digits are rounded off to three significant digits.

Concept introduction:

In a measurement, the significant digits refer to those digits that are known with certainty plus one estimated digit. The digits that are calculated with the help of calculator are nonsignificant digits, which are eliminated by using the process of rounding off.

Answer to Problem 20E

The three significant digits for $1.454\times {10}^1$ is $1.45\times {10}^1$.

Explanation of Solution

Explanation:

The process of rounding off has the following rules:

• When the first nonsignificant digit is less than five, then the remaining nonsignificant digits are dropped.

• When the first nonsignificant digit is greater than or equal to five then to the last number, one significant digit is added, and the remaining nonsignificant digits are dropped.

• The odd-even rule is applied when the nonsignificant digit is five or five followed by zeroes, the last significant digit rounding off when it is odd and when it is even then nonsignificant digits are dropped.

The given non-significant digits are $1.454\times {10}^1$. In the given digits, the number four is dropped. Therefore, the three significant digits for $1.454\times {10}^1$ is $1.45\times {10}^1$.

Conclusion

The three significant digits for $1.454\times {10}^1$ is $1.45\times {10}^1$.

Interpretation Introduction

(b)

Interpretation:

The given nonsignificant digits are rounded off to three significant digits.

Concept introduction:

In a measurement, the significant digits refer to those digits that are known with certainty plus one estimated digit. The digits that are calculated with the help of calculator are nonsignificant digits, which are eliminated by using the process of rounding off.

Answer to Problem 20E

The three significant digits for $1.455\times {10}^2$ is $1.46\times {10}^2$.

Explanation of Solution

The process of rounding off has the following rules:

• When the first nonsignificant digit is less than five, then the remaining nonsignificant digits are dropped.

• When the first nonsignificant digit is greater than or equal to five then to the last number, one significant digit is added, and the remaining nonsignificant digits are dropped.

• The odd-even rule is applied when the nonsignificant digit is five or five followed by zeroes, the last significant digit rounding off when it is odd and when it is even then nonsignificant digits are dropped.

The given non-significant digits are $1.455\times {10}^2$. In the given digits, the number $1.455$ is rounded to $1.46$. Therefore, the three significant digits for $1.455\times {10}^2$ is $1.46\times {10}^2$.

Conclusion

The three significant digits for $1.455\times {10}^2$ is $1.46\times {10}^2$.

Interpretation Introduction

(c)

Interpretation:

The given nonsignificant digits are rounded off to three significant digits.

Concept introduction:

In a measurement, the significant digits refer to those digits that are known with certainty plus one estimated digit. The digits that are calculated with the help of calculator are nonsignificant digits, which are eliminated by using the process of rounding off.

Answer to Problem 20E

The three significant digits for $1.508\times {10}^{-3}$ is $1.51\times {10}^{-3}$.

Explanation of Solution

The process of rounding off has the following rules:

• When the first nonsignificant digit is less than five, then the remaining nonsignificant digits are dropped.

• When the first nonsignificant digit is greater than or equal to five then to the last number, one significant digit is added, and the remaining nonsignificant digits are dropped.

• The odd-even rule is applied when the nonsignificant digit is five or five followed by zeroes, the last significant digit rounding off when it is odd and when it is even then nonsignificant digits are dropped.

The given non-significant digits are $1.508\times {10}^{-3}$. In the given digits, the number $1.508$ is rounded to $1.51$. Therefore, the three significant digits for $1.508\times {10}^{-3}$ is $1.51\times {10}^{-3}$.

Conclusion

The three significant digits for $1.508\times {10}^{-3}$ is $1.51\times {10}^{-3}$.

Interpretation Introduction

(d)

Interpretation:

The given nonsignificant digits are rounded off to three significant digits.

Concept introduction:

In a measurement, the significant digits refer to those digits that are known with certainty plus one estimated digit. The digits that are calculated with the help of calculator are nonsignificant digits, which are eliminated by using the process of rounding off.

Answer to Problem 20E

The three significant digits for $1.503\times {10}^{-4}$ is $1.50\times {10}^{-4}$.

Explanation of Solution

The process of rounding off has the following rules:

• When the first nonsignificant digit is less than five, then the remaining nonsignificant digits are dropped.

• When the first nonsignificant digit is greater than or equal to five then to the last number, one significant digit is added, and the remaining nonsignificant digits are dropped.

• The odd-even rule is applied when the nonsignificant digit is five or five followed by zeroes, the last significant digit rounding off when it is odd and when it is even then nonsignificant digits are dropped.

The given non-significant digits are $1.503\times {10}^{-4}$. In the given digits, the number $1.503$ is rounded to $1.50$. Therefore, the three significant digits for $1.503\times {10}^{-4}$ is $1.50\times {10}^{-4}$.

Conclusion

The three significant digits for $1.503\times {10}^{-4}$ is $1.50\times {10}^{-4}$.