Question

How do you write `297.1` in scientific notation?

Answer 1

`297.1=2.971xx10^2`

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 `297.1` in scientific notation, we will have to move the decimal point two points to left, which literally means dividing by `10^2`. Hence, we have to multiply by `10^2` too along with shifting decimal point.

Hence in scientific notation `297.1=2.971xx10^2`.

Answer 2

`2.971xx10^2`

Explanation:

The objective is to have `color(brown)("just one non zero digit to the left of the ")` `color(brown)("decimal point")`. In doing this we change the value so we have to include a `color(magenta)("mathematical correction")` that, if it were to be applied, would return the new value back to the original number.

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Multiply by 1 but in the form of `1=100/100`

`297.1xx100/100`

Multiplying by 1 in the form of `100/100` does not change the value but it does change the way it looks.

`297.1/100xx100`

`2.971xx100`

`2.971xx10^2`