# Programmed Math/Decimals

Decimals (or floating point numbers) are the oposite of fractions, where fractions take the form of a number over a number eg: ${\displaystyle {\frac {1}{2}}}$ which is one half.

In decimal format this would be 0.5. Why?

Well one half of 1 is 0.5 since 0.5 * 2 is equal to 1. If we multiply the number at the bottom by the decimal we should get the number at the top. Such as:

${\displaystyle {\frac {2}{4}}}$ Is still one half. ${\displaystyle 2/4=0.5}$ since ${\displaystyle {\frac {1}{2}}={\frac {2}{4}}}$ and ${\displaystyle 0.5*4=2}$

So the formulae could be: ${\displaystyle {\frac {a}{b}}=x}$ and thus ${\displaystyle x*b=a}$

## Dividing Decimals

Division by decimals is similar to dividing by whole numbers.

Rebecca enjoys pushing her scooter around the City-park pond after school and on weekends. If she circles the pond 7 times and total distance of 5.88 km, what is the distance around the pond?

To divide a decimal by a whole number, divide the dividend, disregarding the decimal point. Then place the decimal point in the quotient directly above the decimal point in the dividend.

## Steps for Diving with Decimals

The problem of 8 divided 4 was easy enough. We're dealing with two whole numbers, so we just separated 8 into 4 groups to end up with 2 in each group. But what if we have decimals in our division problem? A decimal is a fraction of a whole number written as with as a number with a decimal point. 0.25 is an example of a decimal number.