Chapter 3.1, Problem 10SP

a)

Interpretation Introduction

Interpretation : Each problem is to be solved and to be expressed in scientific notation.

Concept Introduction : A given number is stated as the product of two numbers in scientific notation: a coefficient and 10 raised to a power. The known digits plus the last, estimated digit make up the significant figures in a measurement.

Answer to Problem 10SP

The answer in scientific notation is $1.8\times {10}^1{\text{m}}^2$ .

Explanation of Solution

A given number is stated as the product of two numbers in scientific notation: a coefficient and 10 raised to a power.

Every number bigger than one and less than 10 is a coefficient.

There is an integer exponent.

The given problem is $8.3\text{meters}\times \text{2}\text{.22}\text{meters}$ .

Multiply the number and units.

  $\begin{array}{c}8.3\text{meters}\times \text{2}\text{.22}\text{meters}=\left(8.3\times 2.22\right){\text{m}}^2\\ =18.4{\text{m}}^2\\ =1.8\times {10}^1{\text{m}}^2\end{array}$

b)

Interpretation Introduction

Interpretation : Each problem is to be solved and to be expressed in scientific notation.

Concept Introduction : A given number is stated as the product of two numbers in scientific notation: a coefficient and 10 raised to a power. The known digits plus the last, estimated digit make up the significant figures in a measurement.

Answer to Problem 10SP

The answer in scientific notation is $6.75\times {10}^2\text{m}$ .

Explanation of Solution

A given number is stated as the product of two numbers in scientific notation: a coefficient and 10 raised to a power.

Every number bigger than one and less than 10 is a coefficient.

There is an integer exponent.

The given problem is $8432{\text{meter}}^2÷12.5\text{meters}$ .

Multiply the number and units.

  $\begin{array}{c}8432{\text{meter}}^2÷12.5\text{meters}=\frac{8432{\text{m}}^{\cancel{2}}}{12.5\cancel{\text{m}}}\\ =675\text{m}\\ =6.75\times {10}^2\text{m}\end{array}$

c)

Interpretation Introduction

Interpretation : Each problem is to be solved and to be expressed in scientific notation.

Concept Introduction : A given number is stated as the product of two numbers in scientific notation: a coefficient and 10 raised to a power. The known digits plus the last, estimated digit make up the significant figures in a measurement.

Answer to Problem 10SP

The answer in scientific notation is $\text{5}\text{.87}\times {\text{10}}^{-1}\text{min}$ .

Explanation of Solution

A given number is stated as the product of two numbers in scientific notation: a coefficient and 10 raised to a power.

Every number bigger than one and less than 10 is a coefficient.

There is an integer exponent.

The given problem is $35.2\text{seconds}\times \frac{1\text{minute}}{60\text{seconds}}$ .

Multiply the number and units.

  $\begin{array}{c}35.2\cancel{\text{seconds}}\times \frac{1\text{minute}}{60\cancel{\text{seconds}}}=0.587\text{min}\\ \text{=}\text{5}\text{.87}\times {\text{10}}^{-1}\text{min}\end{array}$