Question

The diameter of the moon is `3,474,000` metres. How is this written in scientific notation?

Answer 1

`3.474 xx 10^6`

Explanation:

scientific notation has only one digit to the left of the decimal point. Then all the other significant digits are written to the right of the decimal point.
The place holders are not written but the function of place holders to show the value of the number is represented by a power of ten.

The `3474` digits are all significant . Having only one digit to the left of the decimal gives `3.474`

The decimal point has been moved six places to the left. This is the same as dividing by `1,000,000` or multiplying by `1/(1,000,000)`

`1/(1000000) xx 1000000 = 1`

`1000 000 = 10^6`

So to keep the value the same the significant digits must be multiplied by `10^6`

the answer is `3.474 xx 10^6`

Answer 2

`3.474 xx 10^6`

Explanation:

Scientific notation is a way of writing very big or very small numbers using powers of `10`.

It is written in the form `a xx 10^n` where `a` is a value such that `1 <=a<10 and n` is an integer.

This means that `a` must have only one (non-zero) digit before the decimal point.

`n` indicates the number of place holders that the decimal point should move.

`1color(blue)(000) = 1 xx 10^color(blue)(3) and 2color(blue)(000) = 2 xx 10^color(blue)(3)`

`3color(blue)(,474,000.) = 3.474 xx 10^color(blue)(6)`

The decimal point is moved `6` places to the left