Question

On average, the planet Pluto's distance from the sun is about 3,670,000,000 miles. How do you express this distance in scientific notation?

Answer 1

In scientific notation, Pluto's distance from the sun is `3.67xx10^9` miles.

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.

Her, we intend to write the large number `3,670,000,000` in scientific notation. To write `3,670,000,000` in scientific notation, as we have a whole number, decimal is at the end the number (as `3` is in fact `3.0`) and we will have to move the decimal point nine points to left, which literally means dividing the large number by `10^9`.

Hence in scientific notation `3,670,000,000=3.67xx10^(9)` (note that as we have moved decimal nine points to the left, to compensate, we are multiplying by `10^9`.

Hence, in scientific notation, Pluto's distance from the sun is `3.67xx10^9` miles.