# How do you write 0.25 million in scientific notation?

Jul 5, 2016

$0.25 m i l l i o n = 2.5 \times {10}^{5}$.

#### Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of $10$.

Note that moving decimal $p$ digits to right is equivalent to multiplying by ${10}^{p}$ and moving decimal $q$ digits to left is equivalent to dividing by ${10}^{q}$.

Hence, we should either divide the number by ${10}^{p}$ i.e. multiply by ${10}^{- p}$ (if moving decimal to right) or multiply the number by ${10}^{q}$ (if moving decimal to left).

In other words, it is written as $a \times {10}^{n}$, where $1 \le a < 10$ and $n$ is an integer.

Now $0 , 25$ million is equivalent to $0.25 \times {10}^{6}$. However, to write in scientific notation, we need to have first digit to the left of decimal and hence we should move the decimal point one point to right, which literally means multiplying by $10$ and also divide by $10$, which will reduce the power of $10$ to $5$.

Hence in scientific notation $0.25 m i l l i o n = 2.5 \times {10}^{5}$.

Jul 6, 2016

$2.5 \times {10}^{5}$

#### Explanation:

A million is ${10}^{6} \to 1000 , 000$

So we have 0.25 of that amount which is written $0.25 \times {10}^{6}$

But scientific notation is such that we have just 1 non zero digit to the left of a decimal point and everything else to the right of it.

So the objective is to and up with $0.25$ becoming $2.5$

But this is a different value. So we include a correction without actually a applying it

$0.25 = 2.5 \times \frac{1}{10}$

So instead of writing $0.25 \times {10}^{6}$ we write:

$2.5 \times \frac{1}{10} \times {10}^{6}$

This is the same as

$2.5 \times \frac{{10}^{6}}{10} \text{ "->" } 2.5 \times {10}^{5}$