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
$$N=0.25\times {10}^6\times {\displaystyle \frac{10}{10}}$$
$$\Rightarrow N=0.25\times 10\times {10}^6\times {10}^{-1}$$
$$\therefore N=2.5\times {10}^5$$

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 $$1\text{ trillion}={10}^{12}$$.