Question

At the start of 2012, the population of the United States was approximately 313,269,000. What is this number written in scientific notation?

Answer 1

`313269000=3.13269xx10^8`

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 `313269000` in scientific notation, we will have to move the decimal point eight point to the left, which literally means dividing by `10^8` for which we should compensate by multiplying it by `10^8`.

Hence in scientific notation `313269000=3.13269xx10^8`.

Answer 2

`3.13269000 xx10^8`

Explanation:

Given:`" "313269000`

Objective: have a single non zero digit to the left of the decimal point. In doing this you have changed the value so a mathematical correction will need to be applied.

Multiply by 1 but in the form of `1=10^8/10^8` giving

`313269000xx10^8/10^8" "larr" this does not change the value"`

`313269000/10^8xx10^8`

`3.13269000 xx10^8" "larr" same value; just looks different!"`

The `10^8` is the mathematical correction which is in place but not applied.