Question

Earth is approximately `9.3×10^7` miles from the sun. If there is a star that is `4.1×10^12` further, how many miles is that star from the earth? Write answer in scientific notation.

Answer 1

`4.100093 xx 10^12` miles

Explanation:

The star that is mentioned is on the other side of the sun, so to find the distance from earth to that star you have add the distances.

Do not be tempted to write the numbers in usual decimal notation - the zeros become tedious, which is why scientific notation is used for big or small numbers,

In algebra: `3x^4 and 8x^4` can be added because they are like terms with the same powers of `x`.

`3x^4 and 8x^4 = 11x^4`

`3x^4 and 8x^5` cannot be added.

The same applies in scientific notation.

`color(blue)(3) xx 10^11 + color(blue)(5) xx 10^11 =color(blue)(8) xx 10^11`

`9.3 xx 10^7 + 4.1 xx 10^12` cannot be added because they have different powers of `x`.

However, by moving the decimal point, we can change the indices and make both powers the same. Move it `5` places to the left.

`9.3 xx10^7 = 0.000093 xx 10^12`

Now you can add:

`4.1color(white)(ww.w)xx10^12`
`ul(0.000093 xx10^12)`
`4.100093 xx 10^12`

The distance from earth to the sun is insignificant in comparison!