Chapter 5, Problem 112A

Interpretation Introduction

Interpretation:

The given number $\text{20}\text{.56120}\text{g}$ needs to be round off to three significant figures.

Concept introduction:

In order to determine the number of significant figures, the following rules should be followed as:

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 greater 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 112A

The given number, $\text{20}\text{.56120}\text{g}$ up to three significant figures is $\text{20}\text{.6}\text{g}$.

Explanation of Solution

The zeros between the non-zero numbers are significant and the last zero of the number is also significant. To round off $\text{20}\text{.56120}\text{g}$ to three significant figures, simply round off the numbers. Here the second digit after the decimal point is less than 5, just remove all the digits after it from the number. The first three numbers are significant. Hence, the given number, $\text{20}\text{.56120}\text{g}$ up to three significant figures is $\text{20}\text{.6}\text{g}$.

Conclusion

The given number, $\text{20}\text{.56120}\text{g}$ up to three significant figures is $\text{20}\text{.6}\text{g}$.