Question

How do you write 3,610,000 in scientific form?

Answer 1

`3,610,000=3.61xx10^7`

Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of `10`.

Note that moving decimal `p` digits to right is equivalent to multiplying by `10^p` and moving decimal `q` digits to left is equivalent to dividing by `10^q`.

Hence, we should either divide the number by `10^p` i.e. multiply by `10^(-p)` (if moving decimal to right) or multiply the number by `10^q` (if moving decimal to left).

In other words, it is written as `axx10^n`, where `1<=a<10` and `n` is an integer.

To write `3,610,000` in scientific notation, we will have to move the decimal point six points to left, which literally means dividing by `10^7`.

Hence in scientific notation `3,610,000=3.61xx10^7` (note that as we have moved decimal one point to right we are multiplying by `10^7` to compensate for division by `10^7`..

Answer 2

`3.61xx10^6`

Explanation:

Taken it 1 step at a time so you can see what is happening.

The multiply by 10's converts the number back to its original state of 3610000

`color(blue)(3610000)`
`color(blue)(361000).0xx10`
`color(blue)(36100).00xx10xx10`
`color(blue)(3610).000xx10xx10xx10`
`color(blue)(361).0000xx10xx10xx10xx10`
`color(blue)(36).10000xx10xx10xx10xx10xx10`
`color(blue)(3).610000xx10xx10xx10xx10xx10xx10color(red)(larr" This one")`

Write as: `3.61xx10^6" "->" "`This has exactly the same value as `" "`3,610,000