Question

How do you convert $75,000,000$ into scientific notation?

Answer 1

Hint: Scientific notation means writing the given number in a decimal format so that only one non zero integer is before the decimal point and without changing the values of the given number. For this we will consider the decimal point at the right most of the given number. Now we will move the decimal point one step before and at the same time we will multiply $10$ 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 simplify it to get the scientific notation.

Complete step by step answer:
Given number, $75,000,000$
Consider the decimal point at the right most of the given number, then the number is
$75,000,000.$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$75,000,000.=75,000,00.0\times 10$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$75,000,000.=750000.00\times 10\times 10$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$75000000=75000.000\times 10\times 10\times 10$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$75000000=7500.0000\times 10\times 10\times 10\times 10$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$75000000=750.00000\times 10\times 10\times 10\times 10\times 10$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$75000000=75.000000\times 10\times 10\times 10\times 10\times 10\times 10$
Moving the decimal one step forward and multiplying the obtained number with $10$ to not disturb the value of given number, then
$75000000=7.5000000\times 10\times 10\times 10\times 10\times 10\times 10\times 10$
In the above equation we have the digit $7$ 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
$75000000=7.5000000\times {{10}^{7}}$
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 $75,000,000$ is $7.5\times {{10}^{7}}$.

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 step. We have another method which will give the result in a single step. If $XXXXXX...$ is a $n$ digited number, then we can write the scientific notation of the number as $XXXXX\cdot \cdot \cdot =X.XXXX\cdot \cdot \cdot \times {{10}^{n-1}}$. From the above formula we can write the eight digit number $75,000,000$ as $7.5000000\times {{10}^{7}}$. From both the methods we got the same result.