Question

How do you write $2.5 \times {10^7}$ in expanded form?

Answer 1

Hint: In order to write the given question $2.5 \times {10^7}$ into its expanded form then , we need to multiply the $2.5$ by ${10^7}$ . And the multiplication of a decimal by tens, hundreds and thousands or etc. itself means that the decimal will be moved to the right side by as many as the number of zeroes are there in the multiplier. If suppose that the decimal number having less digits after the decimal than the multiplier ( or the number of zero is more ) , then the extra zeroes must be added to the final answer as it is . By following these steps we can find the desired result of writing decimal when multiplying and making it in expanded form .

Complete step-by-step solution:
Let we have given a decimal number in the form $2.5 \times {10^7}$ where after decimal there is one digit . Here, in this question we have given decimal as $2.5$ .
So , to calculate the expanded form of the given decimal , we have to first just do the multiplication of decimal value by ${10^7}$ and we get ,
 $2.5 \times {10^7}$

Now the decimal point moves one place to the right from $2.5$ to $25$ . But now the multiplier just used 2 zeroes to overcome the decimal and so we are left with ${10^6}$ as we know the fact that states If the decimal is being moved to the right, the exponent will be negative. That is now we have extra 6 zeroes after moving decimal to right and the exponent becomes \[{10^{7 - 1}} = {10^6}\] .

Now , as per the rule we are just simply going to put the zeroes to the product we got after moving the decimal . Then we are going to get ,
$25 \times {10^6}$
=$25000000$
Therefore the expanded form of$2.5 \times {10^7}$is equal to $25000000$.

Note:
1. Cross-cross your result at least once.
2. To calculate fraction from the percentage , divide the given percentage value by 100
For example : We have to write $70\% $into fraction
$
   = \dfrac{{70}}{{100}} \\
   = \dfrac{7}{{10}} \\
 $
Or
$ = 0.7$
3. If the denominator of the fraction is not possible to make in the form of 10 raised to the power some $n$, then simply divide the fraction by long division to obtain the result.