Chapter 2, Problem 90A

Interpretation Introduction

Interpretation:

The value that determines the number of the significant figures while subtracting $\text{61}\text{.45}\text{g}$ from $\text{242}\text{.6}\text{g}$ needs to be determined.

Concept introduction:

In order to determine the number of significant figures, the following rules should be applied,

1. The non-zero digits are always significant.

2. In a number, the zeros to the left of the first non-zero digit are not significant.

3. Zeros between non zero digits are significant

4. Zeros to the right of the decimal place are significant

5. If a number ends in zero that are not to the right of a decimal,  the zeros may or may not be significant.

To round off a number, look at the digit up to which number needs to be rounded off. If the digit right to it is less than 5 simply add 1 to the previous digit and remove all the digits after it from the number. If the digit right to the digit up to which rounding needs to be done is less than 5, just remove all the digits after it from the number.

Now, if the digit is equal to 5 then 1 is added to the previous digit if it is an odd number. If the previous digit is an even number, simply remove all the digits after it from the number.

Answer to Problem 90A

$\text{242}\text{.6}\text{g}$ number will determine the number of significant figures as it is a least decimal place number.

Explanation of Solution

The number with the least decimal places determines the number of significant figures in the final answer while subtracting. In $\text{242}\text{.6}\text{g}$, the number goes to tenth place while in $\text{61}\text{.45}\text{g}$ goes to hundredth place. This means $\text{242}\text{.6}\text{g}$ number will determine the number of significant figures as it is a least decimal place number and this number is less precise than the other number $\text{61}\text{.45}\text{g}$.

Conclusion

$\text{242}\text{.6}\text{g}$ number will determine the number of significant figures as it is a least decimal place number.