Chapter 2.3, Problem 41PP

(a)

Interpretation Introduction

Interpretation:

The answer of given subtraction problem needs to be rounded off if necessary. $\left(4.32\times {10}^3\text{cm}\right)-\left(1.6\times {10}^4\text{mm}\right)$

Concept introduction:

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 41PP

The final answer of the given problem is correct to $3.0\times {10}^4\text{mm}$.

Explanation of Solution

When subtracting the numbers in scientific notation, the exponent values must be same. Simply, subtract both numbers and keeps the exponent value same. Units should be same for subtracting two measurements.

$4.32\times {10}^3\text{cm}=4.32\times {10}^4\text{mm}$

$\begin{array}{c}\left(4.32\times {10}^4\text{mm}\right)-\left(\text{1}\text{.6}\times {10}^4\text{mm}\right)=\left(4.32-1.6\right)\times {10}^4\text{mm}\\ \text{=}2.72\times {10}^4\text{mm}\\ \text{=}3.0\times {10}^4\text{mm}\end{array}$

Here the second digit is greater than five then add 1 to the digit in the previous place and then remove all the digits to the right.

(b)

Interpretation Introduction

Interpretation:

The answer of given addition problem needs to be rounded off if necessary. $\left(2.12\times {10}^7\text{mm}\right)+\left(1.8\times {10}^3\text{cm}\right)$

Concept introduction:

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 41PP

The final answer of the given problem is correct to $212.2\times {10}^5\text{mm}$.

Explanation of Solution

When adding the numbers in scientific notation, the exponent values must be same. Simply, add both numbers and keeps the exponent value same. Units should be same for adding two measurements.

$\begin{array}{c}1.8\times {10}^3\text{cm}=1.8\times {10}^4\text{mm}\\ \text{=}0.18\times {10}^5\text{mm}\end{array}$

$2.12\times {10}^7\text{mm}\text{=}212\times {10}^5\text{mm}$

$\begin{array}{c}\left(212\times {10}^5\text{mm}\right)-\left(0.18\times {10}^5\text{mm}\right)=\left(212-0.18\right)\times {10}^5\text{mm}\\ \text{=}212.18\times {10}^5\text{mm}\\ \text{=}212.2\times {10}^5\text{mm}\end{array}$

Here the fourth digit is greater than five then add 1 to the digit in the previous place and then remove all the digits to the right.