Chapter 1, Problem 40A

(a)

To determine

The equivalent value of addition of $16.2\text{m}+5.008\text{m}+13.48\text{m}$ .

Answer to Problem 40A

  $34.7\text{m}$

Explanation of Solution

Given:

  $16.2\text{m}+5.008\text{m}+13.48\text{m}$

Calculation:

For the addition of decimals,

Write down the numbers one under the other such that their decimal points are lined up. Then add zeros at the end of the numbers so that each number has same length. Finally, add the numbers using column addition and put the decimal point in the appropriate place in the answer.

Find the addition of $16.2\text{m}+5.008\text{m}+13.48\text{m}$ as follows:

  $\begin{array}{l}16.2\text{m}\\ 5.008\text{m}\\ \underset{\_}{+13.480\text{m}}\\ \underset{\_}{34.688\text{m}}\end{array}$

Round off the result to the least precise value among the measurement-the smallest number of digits to the right of decimal points.

Among the given numbers, the least precision value is $16.2\text{m}$ as it has one digit to the right of the decimal point.

The sum is only precise as the least precise number being added.

Hence, the result of the sum is rounded off to $34.7\text{m}$ .

Conclusion:

Hence, the addition of $16.2\text{m}+5.008\text{m}+13.48\text{m}$ is equal to $34.7\text{m}$ .

(b)

To determine

The equivalent value of addition of $5.006\text{m}+12.0077\text{m}+8.0084\text{m}$ .

Answer to Problem 40A

  $25.022\text{m}$

Explanation of Solution

Given:

  $5.006\text{m}+12.0077\text{m}+8.0084\text{m}$

Calculation:

For the addition of decimals,

Write down the numbers one under the other such that their decimal points are lined up. Then add zeros at the end of the numbers so that each number has same length. Finally, add the numbers using column addition and put the decimal point in the appropriate place in the answer.

Find the addition of $5.006\text{m}+12.0077\text{m}+8.0084\text{m}$ as follows:

  $\begin{array}{l}5.006\text{m}\\ 12.0077\text{m}\\ \underset{\_}{+8.0084\text{m}}\\ \underset{\_}{25.0221\text{m}}\end{array}$

Round off the result to the least precise value among the measurement-the smallest number of digits to the right of decimal points.

Among the numbers, the least precision value is $5.006\text{m}$ as it has only three digits to the right of decimal point.

The sum is only precise as the least precise number being added.

Hence, the result of the sum is rounded off to $25.022\text{m}$ .

Conclusion:

Hence, the addition of $5.006\text{m}+12.0077\text{m}+8.0084\text{m}$ is equal to $25.022\text{m}$ .

(c)

To determine

The equivalent value of subtraction of $78.05{\text{cm}}^2-32.046{\text{cm}}^2$ .

Answer to Problem 40A

  $46.00{\text{cm}}^2$

Explanation of Solution

Given:

  $78.05{\text{cm}}^2-32.046{\text{cm}}^2$

Calculation:

For the subtraction of decimals,

Write down the numbers one under the other such that their decimal points are lined up. Then add zeros at the end of the numbers so that each number has same length. Finally, subtract the numbers using column subtraction and put the decimal point in the appropriate place in the answer.

Find the subtraction of $78.05{\text{cm}}^2-32.046{\text{cm}}^2$ as follows:

  $\begin{array}{l}78.05{\text{cm}}^2\\ \underset{\_}{-32.046{\text{cm}}^2}\\ \underset{\_}{46.004{\text{cm}}^2}\end{array}$

Round off the result to the least precise value among the measurement-the smallest number of digits to the right of decimal points.

Among the measurements, the least precision value is $78.05{\text{cm}}^2$ as it has only two digits to the right of the decimal point.

The subtraction is only precise as the least precise number being involved in subtraction.

Hence, the result of the subtraction is rounded off to $46.00{\text{cm}}^2$ .

Conclusion:

Hence, the subtraction of $78.05{\text{cm}}^2-32.046{\text{cm}}^2$ is equal to $46.00{\text{cm}}^2$ .

(d)

To determine

The equivalent value of subtraction of $15.07\text{kg}-12.0\text{kg}$ .

Answer to Problem 40A

  $3.1\text{kg}$ .

Explanation of Solution

Given:

  $15.07\text{kg}-12.0\text{kg}$

Calculation:

For the subtraction of decimals,

Write down the numbers one under the other such that their decimal points are lined up. Then add zeros at the end of the numbers so that each number has same length. Finally, subtract the numbers using column subtraction and put the decimal point in the appropriate place in the answer.

Find the subtraction of $15.07\text{kg}-12.0\text{kg}$ as follows:

  $\begin{array}{l}15.07\text{kg}\\ \underset{\_}{-12.0\text{kg}}\\ \underset{\_}{3.07\text{kg}}\end{array}$

Round off the result to the least precise value among the measurement-the smallest number of digits to the right of decimal points.

Among the measurements, the least precision value is $12.0\text{kg}$ as it has only one digit to the right of decimal point.

The subtraction is only precise as the least number being involved in subtraction.

Hence, the result of the subtraction is rounded off to $3.1\text{kg}$ .

Conclusion:

Hence, the subtraction of $15.07\text{kg}-12.0\text{kg}$ is equal to $3.1\text{kg}$ .