Question

How do you evaluate `8.13E6 - 7.5E5`?

Answer 1

`8.13xx10^6-7.5xx10^5=color(blue)(7.38xx10^6`

Explanation:

Simplify:

`8.13xx10^6-7.5xx10^5`

In order to add or subtract numbers in scientific notation, they must have the same exponent. You do this by moving the decimal on one of the numbers to make the exponents the same.

It is simpler to convert the number with the smaller exponent to one with the larger exponent. This will keep the answer in correct scientific notation format.

In order to carry out the subtraction above, you can move the decimal in `7.5xx10^5` to the left one place. This will give the number `0.75xx10^6`. Now you can subtract.

`8.13xx10^6-0.75xx10^6=`

`7.38xx10^6`

You can also move the decimal for `8.13xx10^6` one place to the right. This is will give the number `81.3xx10^5`. Now you can subtract the numbers.

`81.3xx10^5-7.5xx10^5=`

`73.8xx10^5`

You now need to move the decimal one place to the left for proper scientific notation format, which will change the exponent to `6`.

`73.8xx10^5=`

`7.38xx10^6`