Question

How do you write $0.25 \times {10^7}$ in standard form ?

Answer 1

In order to write the given question $0.25 \times {10^7}$ into its standard form then , we need to multiply the $0.25$ 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 standard form .

Complete step by step solution:
Let we have given a decimal number in the form where after decimal there are two digits , which is up till hundredth place . Here, in this question we have given decimal as $0.25$ .
So , to calculate the standard form of the given decimal , we have to first just do the multiplication with the decimal value by ${10^7}$ and we get ,
$0.25 \times {10^7}$
Now the decimal point moves two places to the right from $0.25$ to $25$ . But now the multiplier just used 2 zeroes to overcome the decimal and so we are left with ${10^5}$ 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 5 zeroes after moving decimal to right and the exponent becomes ${10^{7 - 2}} = {10^5}$ .
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 ,
$25 \times {10^5}$
=${2500000^{}}$
Hence , the result is ${2500000^{}}.0$ as we moved the decimal places 7 places to the right

Note:
1. Do not Forget to verify the end of the result with the zeroes .
2. If you multiply a decimal with 10 , then the decimal point will be moved to the right side by 1 place
3. If you multiply a decimal with 100 , then the decimal point will be moved to the right side by 2 places .
4. If you multiply a decimal with 1000 , then the decimal point will be moved to the right side by 3 places .
5. If the decimal number has 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 .
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.