How do I figure this out?

Question

If a phone has 10 gigabytes of hard drive space that means it has 10x10⁹ _{bytes of space. A megabyte is 1x10}⁶_.

1. If our phone with 10 gigabytes of free storage downloads a game that takes 76 megabytes, how much free storage is left?
2. Describe the process of subtracting numbers in scientific notation and give the solution.

Thanks.

Answer 1

To add or subtract numbers in scientific notation, all you have to do is make sure that both have the same exponent for the factor of 10. You may have to convert one of the numbers to do that. In this problem you have different factors of 10 for gigabytes and megabytes. Here you have to convert the gigabytes, where 10x10⁹ equals 1000x10⁶. Now you can subtract the numbers because the exponential factors (10⁶) are the same.

1000 - 76 = 924 with a factor of 10⁶, so the answer is 924 x 10⁶ bytes, or 924 megabytes.

Note that in proper scientific notation the number can only have one digit left of the decimal point, so in that form the answer would be 9.24 x 10⁸ bytes.