# How do you convert 0.25 into scientific notation?

Jul 12, 2015

The number in standard scientific notation is 2.5 × 10^(-1).

#### Explanation:

In scientific notation, numbers are written in the form a × 10^b, where $a$ is the "pre-exponential" part and ${10}^{b}$ is the "exponential part".

Your number in decimal form is $0.25$.

To get to "standard" scientific notation, we move the decimal point so there is only one non-zero digit in front of the decimal point.

So, $0.25$ becomes $02.5$.

The leading zero is not significant, so $02.5$ becomes $2.5$.

We moved the decimal point one place, so the exponent is $1$.

We moved the decimal point to the right, so the exponent is negative.

The exponential part is therefore ${10}^{- 1}$.

0.25 = 2.5 × 10^(-1)

Sep 24, 2016

$2.5 \times {10}^{-} 1$

#### Explanation:

One way of approaching this is to write the decimal in fraction form.

$0.25 = \frac{25}{100} = \textcolor{red}{\frac{2.5}{10}}$

Let's use the one given in red, because in scientific notation, we want one non-zero digit before the decimal point.

Using laws of indices we have: $\frac{2.5}{10} = 2.5 \times {10}^{-} 1$

This is exactly what we want!