How do you convert 0.25 into scientific notation?

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Answer 1 · 2015-07-12T23:00:59

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

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 $10^(-1)$ .

$0.25 = 2.5 × 10^(-1)$

Answer 2 · 2016-09-24T11:09:56

$2.5 xx 10^-1$

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

$0.25 = 25/100 = color(red)(2.5/10)$

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: $2.5/10 = 2.5 xx 10^-1$

This is exactly what we want!