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!