Question

How do you convert $7.121\times {{10}^{9}}$ into expanded form?

Answer 1

Hint: The purpose of scientific notation was developed in order to easily represent numbers that are either very large or very small. We can convert them to their standard form also. We use the decimal point in $7.121$ and move it rightwards. To compensate for that we have to multiply the new number with 10 taken from ${{10}^{9}}$. The multiplied form is the standard form of the given number.

Complete step-by-step answer:
The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.
For the given number we move the decimal to the right side one position and bring one zero if there is no such number to cross each time. The decimal keeps going towards right till the power of the 10 becomes 0 from 9. The more we move to the right, the more we multiply with 10.
We explain the first two steps. The decimal starts from its actual position in $7.121$.
Now it crosses the 1 after decimal in $7.121$ which means we have to multiply 10.
So, $7.121$ becomes $71.21$ and ${{10}^{9}}$ becomes ${{10}^{9}}\times {{10}^{-1}}={{10}^{8}}$
Now in the second step the point crosses the 2 in $71.21$. So, $71.21$ becomes $712.1$ and ${{10}^{8}}$ becomes ${{10}^{8}}\times {{10}^{-1}}={{10}^{7}}$.
The movement of the decimal point happens 9 times which means $7.121$ becomes $7121000000$ and ${{10}^{9}}$ becomes ${{10}^{9}}\times {{10}^{-9}}=1$.
Therefore, the standard form of $7.121\times {{10}^{9}}$ is $7121000000$.

Note: In every case where we don’t have any digit to cross or the decimal has reached the rightmost position, we bring an extra 0. For example, in the process when we got $7121$ from $7.121$, we considered $7121$ as $7121.0$ and continued the process. We can start the process with taking extra zeroes at the rightmost position also.