# Fractions to Decimals

### Concept

- The meaning of the word “decimal.”
- Dividing to 1, 2, and 3 decimal places.
- Recognise that fractions and decimals are equivalent
- They say the same thing in different ways.

### Recall

- Simple division with no remainder - say diving 20 oranges between 5 kids.
- Simple division with remainder - say diving 20 oranges between 3 kids.

### Theory

The word “decimal” comes from the Latin word “decimus,” which means “tenth.” When we cannot divide a whole number any further, we break it up into tenths, and hundreths and so on to keep the division going.

Before we see how we do this, it’s important to understand *when* you might end up with a division that results in decimal points:

- When you divide something, and there is a remainder.
- When you divide a smaller number by a larger number.

It can be confusing to divide a *smaller* by a larger number. To divide 3/25 you have to take “25 out of 3.” Now, that’s certainly possible in another Universe, but not this one. In this Universe, you have to extend the numerator with a decimal point and solve the problem. And thus you have a decimal number.

Let’s see the process here:

### Real world applications

Your height, for example is is measured in decimals. You don’t grow from 3 feet to 4 feet overnight. You grow inch by inch. Maybe enough 0.5 inch by 0.5 inch.

Decimals are often needed in word problems like this.

Observe, dear Watson.

- The numbers are increasing by 2.
- There are 4 (not 5!) steps between two numbers.
- So each step is 2/4…1/2…0.5.
- So the arrow is pointing at 10.5