Question

Write the following number in standard form (or scientific notation)
893,000,000

Answer 1

Hint: In the above problem, a number 893,000,000 is given and we have to write its standard form (or scientific notation). There is a general methodology while converting the number into the scientific notation we have to first convert the number into a form in which a number is represented in the form of a number from 1 to 10 then arrange the decimals by multiplying the number with some powers to 10 so that our original number won’t lose.

Complete step-by-step solution:
We are going to write the standard form (or scientific notation) of the number 893,000,000 as follows:
The methodology to write a number into a standard form (or scientific notation) is first of all we have to represent the number from 1 to 10. For e.g. if we have to convert a number which is 4652.39 into standard form then we have to first write the number in the form of 1 to 10 by shifting the decimals in such a way that we can write the number from 1 to 10.
4.65239
As you can see that the above number is in the form of a number which lies in the range of 1 to 10 but if you can see carefully, we lost our original number i.e. 4652.39 so we have to multiply the number by 1000 so the identity of the number won’t lose. So, the number becomes:
$4.65239\times 1000$
Now, if you multiply the number 4.65239 by 1000 we will get the original number i.e. 4652.39.
Using this method in finding the standard form for the number asked in the above question which is 893,000,000. So, first of all, we are representing this number from 1 to 10 by adding decimal to it as follows:
$8.93000000$
Now, to retain the originality of the number we are going to multiply $100000000$ or ${{10}^{8}}$ to the above number and we get,
$8.93000000\times {{10}^{8}}$
Hence, we got the standard form (or scientific form) for 893,000,000 is equal to:
$8.93000000\times {{10}^{8}}$

Note: There is a trick to find the standard notation of a number is that if your number is greater than 10 then the numbers you crossed from the already given decimal point or no decimal point to put a decimal in the given number is the same as the power that you put in 10.
For e.g. in the above problem, we have given a number 893,000,000 so we have crossed 8 numbers to put a decimal after the number 8 and you can see that power of 10 is also 8.
Let us take a number which is a decimal number already but greater than 10 say 126.435. Now, we are going to convert this number into a standard form so first of all we are putting decimal after 1.
1.26435
For that we have crossed 2 numbers (i.e. 2 and 6). Now, we have to multiply some power of 10 so we will multiply ${{10}^{2}}$ to the above number because we have crossed two numbers (2 and 6) so the power of 10 should be 2.
\[1.26435\times {{10}^{2}}\]