# Wikijunior:Introduction to Mathematics/Decimals

## New Words

• Almost-equal sign
• Decimal number
• Decimal place

## Lesson

### Why use Decimals?

Some fractions have big numbers and are difficult to use. For example, which of the next fractions is the most?

• ${\displaystyle {\frac {44467}{38973}}}$

• ${\displaystyle {\frac {82489}{71035}}}$

• ${\displaystyle {\frac {8993}{7873}}}$

Show the fractions as mixed fractions and it might be easier to answer which is most.

• ${\displaystyle {\frac {44467}{38973}}}$ = ${\displaystyle 1{\frac {5494}{38973}}}$

• ${\displaystyle {\frac {82489}{71035}}}$ = ${\displaystyle 1{\frac {11454}{71035}}}$

• ${\displaystyle {\frac {8993}{7873}}}$ = ${\displaystyle 1{\frac {1120}{7873}}}$

It is still difficult to answer which is most. A different way to show fractions makes answering easier.

### Decimal Numbers

Decimals Numbers have two parts, the same way that mixed numbers have two parts. The two parts are separated by a small circle called a decimal point. The part of the decimal number to the right of the decimal point is the fraction part. The part to the left is the whole part. The way you find the decimal form of a number is by dividing by hand or using a calculator. These are examples of fractions in decimal form:

• ${\displaystyle {\frac {3}{2}}=1.5}$

• ${\displaystyle {\frac {1}{5}}=0.2}$

• ${\displaystyle {\frac {1}{10}}=0.1}$

• ${\displaystyle {\frac {51}{25}}=2.04}$

• ${\displaystyle {\frac {1}{40}}=0.025}$

• ${\displaystyle {\frac {1}{100}}=0.01}$

Just like place amounts made it easy to show big normal numbers, decimal places make it easy to show fractions with big numbers. Note: one tenth = ${\displaystyle {\frac {1}{10}}}$, one hundredth = ${\displaystyle {\frac {1}{100}}}$

 ${\displaystyle .}$4${\displaystyle 62897}$ 4 tenths ${\displaystyle .4}$6${\displaystyle 2897}$ 6 hundredths ${\displaystyle .46}$2${\displaystyle 897}$ 2 thousandths ${\displaystyle .462}$8${\displaystyle 97}$ 8 ten thousandths ${\displaystyle .4628}$9${\displaystyle 7}$ 9 hundred thousandths ${\displaystyle .46289}$7 7 millionths

### Almost Equal

Sometimes when you change a fraction to a decimal the number will never end. For example, ${\displaystyle {\frac {1}{3}}}$ becomes 0.33333333333333333333333… and the threes repeat forever. Because you can not write a number that goes on forever, you use only as much as you need for answering your math question.

When you remove a part of a number it is no longer the same number, but because the new number is almost the same as the old number, you can still use it to answer questions about the old number. The almost equal sign (≈) is a special sign you use for when two numbers are almost the same. For example: ${\displaystyle {\frac {1}{3}}\approx 0.333333}$

### Which is the most?

Using decimal numbers it is now easy to find which fraction is the most.

• ${\displaystyle {\frac {44467}{38973}}\approx 1.140969389064}$

• ${\displaystyle {\frac {82489}{71035}}\approx 1.161244456958}$

• ${\displaystyle {\frac {8993}{7873}}\approx 1.142258351327}$

Because there is a 6 in the hundredths place you know the second fraction is most.