Question

Write $8.2 \times {10^5}$ in standard notation?

Answer 1

Hint: We are given a number and we have to write it in standard form. But the number given is already in standard notation so we will convert it in 'Common form' to convert from Standard notation to common form. By moving the decimal to the right the number of places indicated by 10's exponent. If the exponent is negative or in case of negative exponent move the decimal to the left and if digits are less then put zero. We are given a number of positive exponents so we will apply the first method.

Complete step by step answer:
Step1:
We are given a number $8.2 \times {10^5}$ in a standard notation and we have to convert it into common form. As the exponent is positive so we will place the decimal to the right. As the digits are less in comparison to the exponent number so we will place the zero. As the exponent is 5 so we will place five extra zeroes.
$ \Rightarrow 8.2 \times {10^5} = 8.2 \times {100000}$

Step2:
As the exponent is 5 we will move the decimal right to five places we will get:
$ \Rightarrow 8.2 \times {10^5} = 820000.0$

Note: In this type of questions when standard notation is given and if they ask you to convert to standard notation. To convert the expression in common form. There can be two forms of standard notation in one case exponent is positive and in other cases exponent is negative. For positive exponent move the decimal to the right and for negative decimal move it to the left if digits are less in the number than number in exponents. We can place the zero before the digits if we are moving towards left and after the digits in case of moving right. This is the only procedure to solve these types of questions.