Chapter 3.1, Problem 1SP

a)

Interpretation Introduction

  $\left(6.6\times {10}^{-8}\right)+\left(5.0\times {10}^{-9}\right)$

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

Concept Introduction :

The known digits plus the last, estimated digit make up the significant figures in a measurement.

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

Answer to Problem 1SP

The answer to the problem in scientific notation is $7.1\times {10}^{-8}$ .

Explanation of Solution

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

There is an integer exponent.

In the case of an addition, the exponents must be the same otherwise they should be aligned and then the addition is carried out.

The given problem is $\left(6.6\times {10}^{-8}\right)+\left(5.0\times {10}^{-9}\right)$ .

The exponents are first aligned to the same power.

  $\left(6.6\times {10}^{-8}\right)+\left(5.0\times {10}^{-9}\right)=\left(6.6\times {10}^{-8}\right)+\left(0.5\times {10}^{-8}\right)$

Add the coefficients.

  $\begin{array}{c}\left(6.6\times {10}^{-8}\right)+\left(5.0\times {10}^{-9}\right)=\left(6.6\times {10}^{-8}\right)+\left(0.5\times {10}^{-8}\right)\\ =\left(6.6+0.5\right)\times {10}^{-8}\\ =7.1\times {10}^{-8}\end{array}$

b)

Interpretation Introduction

  $\left(9.4\times {10}^{-2}\right)-\left(2.1\times {10}^{-2}\right)$

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

Concept Introduction :

The known digits plus the last, estimated digit make up the significant figures in a measurement.

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

Answer to Problem 1SP

The answer to the problem in scientific notation is $7.3\times {10}^{-2}$ .

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.

In the case of subtraction, the exponents must be the same otherwise they should be aligned and then the subtraction is carried out.

The given problem is $\left(9.4\times {10}^{-2}\right)-\left(2.1\times {10}^{-2}\right)$ .

Since the exponents are the same, the coefficients are subtracted.

  $\begin{array}{c}\left(9.4\times {10}^{-2}\right)-\left(2.1\times {10}^{-2}\right)=\left(9.4-2.1\right)\times {10}^{-2}\\ =7.3\times {10}^{-2}\end{array}$