MATH SOLVE

2 months ago

Q:
# What's 3.3022 × 10 to the 23rd power plus 4.8685 × 10 to the 24th power plus 5.9722 × 10 to the 24th power plus 6.4185 × 10 to the 23rd power divided by 4?

Accepted Solution

A:

All numbers are to the 23rd or 24th power, it helps if you rewrite the numbers so they have the same magnitude. You can do this by moving the decimal point one digit to the right for every 1 you subtract from the exponent.
4.8685 Ă— 10^24 = 48.685 * 10^23.
5.9722 Ă— 10^24 = 59.722 * 10^23.
Now that all exponent are the same you can ignore them and add them back after doing the calculations. I am doing the operations in the order that they are described. If it is written as a sum without parenthesis the division would have precedence over the additions.
(3.3022 + 48.685 + 59.722 + 6.4185) / 4 = 29.531925.
All the numbers we started with have 5 significant digits so we should round our answer to 5 significant digits as well. Now we add back the 10 to the 23rd power part and we get 29.531 * 10^23.
The solution has two digits before the decimal point, we can fix this by changing the exponent to 24 and moving the decimal point one place to the right.
The final result will then be: 2.9531 * 10^24.