Question

How do you write `8.32 times 10^ -2` in standard notation?

Answer 1

In standard notation it is `0.0832`.

Explanation:

Scientific notation is a way to abbreviate numbers that would be really LONG otherwise, either very large numbers or very small ones. It uses the exponent to tell you how many places to move the decimal point and in which direction, to get the number back in standard notation.

A negative exponent means the number is smaller than it looks. Here, it's smaller than `8.32`

The exponent `- 2` means we have to move the decimal point two places to the LEFT.
Doing that gives us `0.0832`.

If the number in scientific notation were `8.32` x `10^2`, you would move the decimal point two places to the RIGHT, giving you:
`8,320`, or `8,320.00` in standard notation.

Suppose you had to write a report about the national debt, which is in the trillions of dollars I think. Would you want to have to write all those zeros every time?

Instead, you could use scientific notation. Let's pretend the debt is 2 trillion dollars. You can write this as:

`2.0 xx10^12`

since two trillion is a 2 followed by 12 zeros.