Question

How do you write \[652.9\times {{10}^{5}}\] in standard notation?

Answer 1

Hint: We are given a number. And we have to write the given number in the standard notation. To write the number in the standard notation, we just have to expand the power raised to 10, that is, \[{{10}^{5}}=100000\]. So, when the term \[652.9\] is multiplied by \[100000\], the decimal point will shift five places towards the right and we will get the standard notation for the given number.

Complete step by step solution:
According to the given question, we are given a number. As per the given question, we have to write the given number in standard notation.
The given number we have is,
\[652.9\times {{10}^{5}}\]
As we can see that, the number has a term \[652.9\] which is multiplied to \[{{5}^{th}}\] power raised to 10. In order to write the given number in the standard form, we will have to expand the power raised to 10.
For example - \[{{10}^{2}}=100\], that is, hundred is represented as the \[{{2}^{nd}}\] power raised to 10.
So, we have, \[{{5}^{th}}\] power raised to 10 and it is given as, \[{{10}^{5}}\] and it is equivalent to \[100000\].
We can write it as,
\[{{10}^{5}}=100000\]
Now, we have to multiply the term \[652.9\] by \[100000\]. While doing so, the decimal point will shift from its current position to 5 decimal places towards the right. We get the number as,
\[652.9\times 100000\]
Now, shifting the decimal places towards the right, we will have,
\[\Rightarrow 65290000.0\]
We can write it as,
\[\Rightarrow 65290000\]
Therefore, the standard notation of the given number is \[65290000\].

Note: The power to which 10 is raised should be correctly written and used while doing the multiplication. While carrying out the multiplication, the decimal place is shifted towards the right, but in case of division, the decimal place is shifted towards the left.