Chapter 6, Problem 95A

a.

To determine

Multiplication of the given expression with correct significant figure.

Answer to Problem 95A

Multiplication will be $21\times {10}^{15}{\text{m}}^2$ .

Explanation of Solution

Given:

The given expression is

  $\left(5\times {10}^8\text{ m}\right)\times \left(4.2\times {10}^7\text{ m}\right)$

Formula used :

When two numbers are multiplied then number of significant in their multiplication is equal maximum number of significant figure in the given expression.

Calculation:

In the given expression maximum significant figure is 2.

Therefore, in multiplication of the expression number of significant figure will be also equal to 2.

Now,

  $\begin{array}{c}\left(5\times {10}^8\text{ m}\right)\times \left(4.2\times {10}^7\text{ m}\right)=5\times 4.2\times {10}^{8+7}\\ =21\times {10}^{15}{\text{m}}^2\end{array}$

Conclusion :

Therefore, product of the given expression with correct significant number will be, $21\times {10}^{15}{\text{m}}^2$ .

b.

To determine

Multiplication of the given expression with correct significant figure.

Answer to Problem 95A

Multiplication will be $14.2\times {10}^{-8}{\text{ km}}^2$ .

Explanation of Solution

Given:

The expression is

  $\left(1.67\times {10}^{-2}\text{ km}\right)\times \left(8.5\times {10}^{-6}\text{ km}\right)$

Formula used :

When two numbers are multiplied then number of significant in their multiplication is equal maximum number of significant figure in the given expression.

Calculation:

In the given expression maximum significant figure is 3.

Therefore, in multiplication of the expression number of significant figure will be also equal to 3.

Now,

  $\begin{array}{c}\left(1.67\times {10}^{-2}\text{ km}\right)\times \left(8.5\times {10}^{-6}\text{ km}\right)=1.67\times 8.5\times {10}^{-2-6}\\ =14.195\times {10}^{-8}\\ =14.2\times {10}^{-8}{\text{ km}}^2\end{array}$

Conclusion :

Therefore, product of the given expression with correct significant number will be, $14.2\times {10}^{-8}{\text{ km}}^2$ .

c.

To determine

Division of the given expression with correct significant figure.

Answer to Problem 95A

Division will be equal to $2.8{\text{ kg/m}}^3$

Explanation of Solution

Given:

Expression is,

  $\frac{2.6\times {10}^4\text{ kg}}{9.4\times {10}^3{\text{ m}}^3}$

Formula used :

When two numbers are divided then number of significant in their division is equal maximum number of significant figure in the given expression.

Calculation:

In the given expression maximum significant figure is 2.

Therefore, in division of the expression number of significant figure will be also equal to 2.

Now,

  $\begin{array}{c}\frac{2.6\times {10}^4\text{ kg}}{9.4\times {10}^3{\text{ m}}^3}=0.276\times {10}^{4-3}\\ =0.276\times 10\\ =2.76{\text{ kg/m}}^3\\ =2.8{\text{ kg/m}}^3\end{array}$

Conclusion :

Therefore, division of the given expression with correct significant figure is, $2.8{\text{ kg/m}}^3$ .

d.

To determine

Division of the given expression with correct significant figure.

Answer to Problem 95A

Division will be equal to $\text{1}\text{.8}\times {\text{10}}^{-3}\text{ m/sec}$ .

Explanation of Solution

Given:

Expression is $\frac{6.3\times {10}^{-1}\text{ m}}{3.8\times {10}^2\text{ sec}}$

Formula used :

When two numbers are divided then number of significant in their division is equal maximum number of significant figure in the given expression.

Calculation:

In the given expression maximum significant figure is 2.

Therefore, in division of the expression number of significant figure will be also equal to 2.

Now,

  $\begin{array}{c}\frac{6.3\times {10}^{-1}\text{ m}}{3.8\times {10}^2\text{ s}}=1.657\times {10}^{-1-2}\text{ m/s}\\ \text{=1}\text{.7}\times {\text{10}}^{-3}\text{ m/s}\end{array}$

Conclusion :

Therefore, division of the given expression with correct significant figure is $\text{1}\text{.7}\times {\text{10}}^{-3}\text{ m/s}$ .