Question

In standard form 52,00,00,000 is equal to
A) \[5.2 \times {10^7}\]
B) \[5.2 \times {10^8}\]
C) \[52 \times {10^8}\]
D) \[52 \times 100,00,000\]

Answer 1

Hint: The number given is in general form. When we write it in standard form we use powers of 10. All zeros are written in the form of powers of 10. Also sometimes we use decimal also and increase the power of 10 by 1. And this is increased as the decimal shifts to left. Now let’s solve it!

Complete step by step solution:
Given the number is 52,00,00,000.
Now the zeros if separated then the same number can be written as
\[ \Rightarrow 52 \times 100,00,000\]
But since we want to write this number in standard form we will use powers of ten as
\[ \Rightarrow 100,00,000 = {10^7}\]
So the number can be written as
\[ \Rightarrow 52 \times {10^7}\]
But this is not available as an option. but shifting the decimal point to left by one decimal place we get,
\[ \Rightarrow 5.2 \times 10 \times {10^7}\]
\[ \Rightarrow 5.2 \times {10^8}\]
This is the option available. Thus the standard form is \[ 5.2 \times {10^8}\]

Thus the correct option is B.

Note:
Here students should note that though the options are similar looking the powers or decimal place may change. Like talking about option D and B. Both are the ways in which the given number can be written. But we need to write it in standard form so we chose option B as the correct one.
One more thing is to be noted that option B and C are only differing in a decimal point but it causes a big difference in answer. So choose your answer wisely!