Chapter 2, Problem 88A

Interpretation Introduction

Interpretation:

The two numbers from the given set of three numbers which produce same number when rounded off to the three significant figures 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 88A

$\text{3}\text{.450}$ and $\text{3}\text{.448}$ will produce a same number when rounded off to the three significant figures.

Explanation of Solution

Given information:

The given numbers are as follows:

$\text{3}\text{.456,}\text{3}\text{.450}\text{or}\text{3}\text{.448}$

The number $3.450$ will remain same when rounded off to three significant figures. The fourth digit in the other two numbers is greater than 5. Therefore, other two numbers will be rounded off to $\text{3}\text{.46}$ and $\text{3}\text{.45}$ which are different from the original given values. Hence, $\text{3}\text{.450}$ and $\text{3}\text{.448}$ will produce a same number when rounded off to the three significant figures that is 3.45.

Conclusion

$\text{3}\text{.450}$ and $\text{3}\text{.448}$ will produce a same number when rounded off to the three significant figures.