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Scientific notation, which uses exponents to compress large numbers, is remarkably simple.

is a shorter way of writing the number 1,670,000,000,000,000,000,000.

Because the exponent in this case is 21, we moved the decimal point in the number 1.67 to the right by 21 spaces, adding as many zeros on the right as we needed.

If the exponent had been a negative number, say 1.67x10-15,

we would move the decimal point to the left instead, adding as many zeros to the left as we need (15 in this case).

0.00000000000000167

0.25  = 2.5 x 10-1 

0.00000025  =  2.5 x 10-7 

Using the example above, the story might read “1.67 times 10 to the power of 21”.

Negative numbers in an exponent refer to tiny fractions.

For instance,

is the same as .0000035   The decimal point moved left by 6 spaces.  The whole point of scientific notation is to make things clearer and simpler.  Once you get the idea and start using it, it is (almost) never confusing.

Exponents make news simpler

Adding and multiplying with exponents

Numbers written in scientific notation are very easy to multiply and to add.

Multiplication with exponents:

10 3 (a million) times 10 9 (a billion) is 10 12 .  You just add the exponents to multiply the values.   If there are numbers before the 10 (like 1.67 for instance) you multiply those together while adding the exponents.

Addition with exponents:

3 x 10e2   plus  6 x 10e2 =  9 x 10e2   Just add the 3 and the 6.

For this to work, the exponents for each of the numbers must be the same.

As consumers of the news we won’t be called on to do this very often, but it’s nice to know that exponents are useful as well as cute.

The converters below will help you transform numbers written with exponents into something  possibly more tangible and interesting.

In order to make it work, you need to re-write your exponential number in a form that a calculator recognizes.

To tell the converter that you have an exponent, simply enter the letter ‘e’ and then the exponent. 

becomes 1.67e21. You leave out the ‘x 10’ part.

Volume

Bring exponential numbers to life: