Question

What is $93,000,000$ in scientific notation?

Answer 1

Hint: In this problem we need to convert the given number into scientific notation. We know that scientific notation means writing the given number in a decimal format so that only one non zero integer is present before the decimal point and without changing the value of the given number. For this we will consider the decimal point at the right most end of the given number. Now we will move the decimal point one step before along with multiplying $10$ with the given number. We will continue this process up to where we will have only one non zero digit before the decimal point and apply exponential formulas to simplify the value.

Complete step-by-step answer:
Given number, $93,000,000$
Consider the decimal point at the right most of the given number, then the number is
$93,000,000.$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$93,000,000.=93,000,00.0\times 10$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$93,000,000.=930000.00\times 10\times 10$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$93,000,000=93,000.000\times 10\times 10\times 10$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$93,000,000=9,300.0000\times 10\times 10\times 10\times 10$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$93,000,000=930.00000\times 10\times 10\times 10\times 10\times 10$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$93,000,000=93.000000\times 10\times 10\times 10\times 10\times 10\times 10$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$93,000,000=9.3000000\times 10\times 10\times 10\times 10\times 10\times 10\times 10$
In the above equation we have the digit $9$ which is a non-zero integer before the decimal point. So, we will stop moving the decimal point. Now we will simplify the above equation by using an exponential rule which is $a.a.a.a....\text{ }n\text{ times}={{a}^{n}}$, then we will get
$93,000,000=9.3000000\times {{10}^{7}}$
We know that there is no value for zero which is placed after the decimal, so we can neglect them.
Hence the scientific notation of the number $93,000,000$ is $9.3\times {{10}^{7}}$.

Note: In the problem we have an eight digit number, so we have done so many moving operations to get the result. But it is not necessary to follow the above procedure to convert a number into scientific notation. We have another method which will give the result in a single step. Suppose we need to convert a $n$ digit number which is represented by $xxxxxx....$ into scientific notation, then simplify place a decimal point after one digit from the left side and multiply the number with ${{10}^{n-1}}$. Then we will get scientific notation of $xxxxxx....$ as $xxxxxx....=x.xxxxxx.....\times {{10}^{n-1}}$.