Question

What is `3.23*10^12` in standard form?

Answer 1

`color(green)(3,230,000,000,000)`

Explanation:

`10^12 = 1,000,000,000,000`
So
`3.23*10^12 = 3,230,000,000,000`

Answer 2

In standard form, `3.23*10^12` would look something like this:
`3,230,000,000,000`.

Explanation:

First of all, standard form basically means writing out a number as it would normally look. For instance, it would be just like writing the number 0.002 or 450.

In addition, in often times you might be asked to write a number from scientific notation to standard form. An example of how this would look like can be seen below.

(e.g.) Scientific Notation: `(1) 4*10^7` `(2) 4*10^-2`
Standard Form: `(1) 40,000,000` `(2) 0.04`

Moreover, when changing a number from scientific notation to standard form you have to move the decimal point either to the right or to the left depending on whether the exponent is positive or negative.

For instance, looking at the problem `3.23*10^12`, you can solve it by multiplying `3.23` by `10^12`. In other words, since the exponent is `12`, you can move the decimal point 12 places to the right*.
(e.g. of moving the decimal point)

In conclusion, if done correctly, the final result should be `3,230,000,000,000`.

*When you multiply a number by `10^n`, where `n` is positive, the decimal point of the number moves `n` places to the right.

When you multiply a number by `10^n`, where `n` is negative, the decimal point of the number moves `n` places to the left.

Answer 3

`3230000000000" "->" "3,230,000,000,000`

Explanation:

I elected to show it this way to give you a feel of how multiplying by 10's works .

`3.23xx10^12" "->3.23xx10xx10^11 = 32.3xx10^11`
`32.3xx10^11" "->32.3xx10xx10^10 = 323xx10^10`
`323xx10^10" "->323color(white)(.)xx10xx10^9=3230xx10^9`
`3230xx10^9" "->3230xx10xx10^8=32300xx10^8`

This continues until you end up with:

`color(red)(323xx10^10)=3230000000000`
`color(red)(" "ul(|" "|))`
`color(red)(" "uarr)`
`color(purple)(" 10 zeros")`