Chapter 2, Problem 1SAQ

Express the number 0.000042 in scientific notation.

a. $0\cdot 42\times {10}^{-4}$

b. $4\cdot 2\times {10}^{-5}$

c. $4\cdot 2\times {10}^{-4}$

d. $4\times {10}^{-5}$

Interpretation Introduction

Interpretation: The number $0.000042$ is to be expressed in scientific notation.

Concept Introduction: Scientific notations are used to express too big and too small numbers in a decimal form for better representation of the number. It simplifies the calculations. According to this notation, all numbers are expressed in the following manner:

$m\times {10}^n$.

Here, $m$ is called decimal part, that is any real number lying between $1$ and $10$ and ${10}^n$ is an exponent part where, n is an integer.

Answer to Problem 1SAQ

Correct answer: The given number $0.000042$ in a scientific notation is expressed as $4.2\times {10}^{-5}$. Therefore, option (b) is the correct answer.

Explanation of Solution

Reason for correct option:

The given number is $0.000042$. To express this number in a scientific notation, the value of $m$ will be between $1$ and $10$. For obtaining the value of $m$, the decimal point is moved to right 5 decimal places, thus, decimal part, $m$ is $4.2$ and the exponent part is $5$. Since, the decimal point is moved to the right, the sign of the exponent is negative i.e. $-5$.

Thus, it is written as $4.2\times {10}^{-5}$.

Reasons for incorrect options:

The number $0.000042$ in a scientific notation cannot be expressed as $0.42\times {10}^{-5}$. Therefore, option (a) is incorrect.

The number $0.000042$ in a scientific notation cannot be expressed as $4.2\times {10}^{-4}$. Therefore, option (c) is incorrect.

The number $0.000042$ in a scientific notation cannot be expressed as $4\times {10}^{-5}$. Therefore, option (d) is incorrect.