Question

How do you write \[0.25\] million in scientific notation?

Answer 1

Hint: We are given a number and asked to write the number in scientific notation. First recall the form of a number in scientific notation. Then try to form the given number in such form, also here million terms are given so remember to take it in power of \[10\].

Complete step by step solution:
Given, the number \[0.25\] million. We are asked to write this number in scientific notation.In scientific notation we write a number in such a way that there is only one digit to the left of decimal or before decimal point and it is multiplied by an integer power of \[10\], that is a number in scientific notation is written as, \[N = a \times {10^b}\].

We have the number as, \[N = 0.25{\text{ million}}\].
One million is equal to \[{10^6}\].
Therefore, the number can be written as,
\[N = 0.25{\text{ million}} = 0.25 \times {10^6}\]
In scientific notation there should be only one digit before decimal point. Here, the number is \[0.25 \times {10^6}\] and we observe that there is no number before decimal point so to bring \[2\] before decimal point we multiply and divide the number by \[10\], that is
\[N = 0.25 \times {10^6} \times \dfrac{{10}}{{10}}\]
\[ \Rightarrow N = 0.25 \times 10 \times {10^6} \times {10^{ - 1}}\]
\[ \therefore N = 2.5 \times {10^5}\]

Therefore, \[0.25\] million in scientific notation is \[2.5 \times {10^5}\].

Note: Scientific notation is used to write very large numbers or very small numbers. Here we got the number as \[2.5 \times {10^5}\] which is a very large number. If the power of \[10\] is positive then the number is a large number and if the power of \[10\] is negative then the number is a small number. Also, here the term million is used, there are two more such terms known as billion and trillion, these are written as, \[1{\text{ billion}} = {10^9}\] and \[1{\text{ trillion}} = {10^{12}}\].