Chapter 5.1, Problem 1RQ

Interpretation Introduction

Interpretation: The exponents for writing numbers using scientific notations in case of numbers greater and less than 1 needs to be determined.

Concept introduction: The scientific notation represents very large and very small numbers. It contains two parts one is any number between 1 and 10 (including 1 but not 10) and other is base of 10 with exponent.

Explanation of Solution

For numbers greater than 1, the exponent can be obtained by moving decimal to the left thus; exponent will be a positive integer. Similarly, for numbers less than 1, the exponent can be obtained by moving decimal to the right thus, exponent will be a negative integer.

For example, a number greater than 1 can be 5261 here; exponent can be obtained by moving decimal to the left because the first part should be any number between 1 and 10 (including 1). The decimal will move 3 places to the left to obtain 5.261. Since, decimal is moved 3 places to the left thus, exponent will be +3.

The scientific notation for number will be $5.261\times {10}^{+3}$ or, $5.261\times {10}^3$ .

Similarly, a number less than 1 can be 0.5261. To place decimal after first non-zero digit, decimal should be moved 1 place to the right and number obtained will be 5.261. Since, the decimal is moved 1 place to right, the exponent will be -1.

The scientific notation for number will be $5.261\times {10}^{-1}$ .