Chapter 3.1, Problem 2SP

Interpretation Introduction

Interpretation : The given 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 2SP

The answer in scientific notation is $3.0\times {10}^4$ .

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,

  $\frac{\left(6.6\times {10}^6\right)}{\left(8.8\times {10}^{-2}\right)\times \left(2.5\times {10}^3\right)}$

The multiplication sign is used in the denominator, so the coefficients are multiplied while the exponents are added up.

The division sign is used between the numerator and denominator; so, the coefficients are divided while the exponents are subtracted.

There are two terms in the denominator, so first, these are multiplied followed by the division in the numerator by the denominator.

Consider the terms $\left(8.8\times {10}^{-2}\right)\times \left(2.5\times {10}^3\right)$ .

The coefficients are multiplied and the exponents are added up.

  $\begin{array}{c}\left(8.8\times {10}^{-2}\right)\times \left(2.5\times {10}^3\right)=\left(8.8\times 2.5\right)\times \left({10}^{-2+3}\right)\\ =22\times {10}^1\\ =2.2\times {10}^2\end{array}$

The question is rewritten as

  $\frac{\left(6.6\times {10}^6\right)}{\left(8.8\times {10}^{-2}\right)\times \left(2.5\times {10}^3\right)}=\frac{\left(6.6\times {10}^6\right)}{\left(2.2\times {10}^2\right)}$

Now, solve $\frac{\left(6.6\times {10}^6\right)}{\left(2.2\times {10}^2\right)}$ .

The coefficients are divided and the exponents are subtracted.

  $\begin{array}{c}\frac{\left(6.6\times {10}^6\right)}{\left(2.2\times {10}^2\right)}=\frac{\left(6.6\right)}{\left(2.2\right)}\times {10}^{6-2}\\ =3.0\times {10}^4\end{array}$