Question

How do you write \[25,000,000,000,000\] in scientific notation?

Answer 1

Hint:In this question, we have to convert a given number that is written in standard form into scientific notation. The method of expressing too large or too small numbers in the decimal form for a convenient expression is known as scientific notation. When a number is written as a product of a number lying between 1 and 10 and a power of 10, it is said to be in scientific notation. An example of scientific notation is $N \times {10^m}$ where N lies between 1 and 10 and involves only significant figures.
For writing a number in scientific notation, we have to place the decimal point after the first digit so we divide and multiply the given number with a power of 10 such that the power is equal to (total number of digits – 1). The digits after the decimal point are rounded off
because the scientific notation should contain only significant figures.

Complete step by step answer:
There are fourteen digits in the given number so we multiply and divide the number by ${10^{13}}$ ,
so we get –
\[
\Rightarrow 25,000,000,000,000 \times \dfrac{{{{10}^{13}}}}{{{{10}^{13}}}} \\
\Rightarrow 2.5 \times {10^{13}} \\
\]
Note: We simply multiply the decimal number with the power of 10 for converting the scientific notation into standard form. In the given question, while finding the scientific notation; we see that there are two significant figures so a decimal is involved. This way we can solve similar questions. ${10^{13}}$ means 10 multiplied with itself 13 times, there are 12 zeros in the given number so 12 of the zeros will cancel out and the remaining one zero is used as a decimal.