Where are fractions and decimal numbers on the number line?

Let's review what we know about whole numbers Let's review what we know about whole numbers. When we add numbers in a sequence like 1, 2, 3, we can keep on counting by adding one to each number.

The gaps between whole numbers are another set of numbers.

These numbers are either fractions or decimal numbers.

The numbers between 7 and 8 are fractions and there are an infinite number of them.

We can describe the place halfway between 7 and 8 using the fraction 7 and a half…

…or the decimal number seven and five tenths …or the decimal number seven and five tenths. We can see that fractions and decimals can be different names for the same place on a number line.

Let's look at some common fractions and decimal numbers between the whole numbers 10 and 11 on this number line.

The decimal numbers 10 and 25 hundredths, 10 and 5 tenths, and 10 and 75 hundredths…

Have the same values as the fractions 10 and one fourth, ten and one half, and 10 and three fourths.

Lets look at some other common fractions and decimal numbers between the numbers 10 and 11.

The decimal numbers ten and 33 hundredths and 10 and 67 hundredths…

…have the same value as the fractions 10 and one third and ten and two thirds.

There are an infinite number of fractions and decimals between any two numbers.

When we find any two fraction or decimal numbers, we know there are always others between them. Here we see the fractions 1/2 and 3/4 with their equivalent decimal numbers.

When we add fractions or decimals between whole numbers, it is not always predictable. We add 5/8 here because it is larger than ½ but smaller than 3/4.

We can find more fractions and decimals between 5/8 and 3/4 We can find more fractions and decimals between 5/8 and 3/4. 2/3 is larger than 5/8 (HL 5/8 and decimal) and smaller than 3/4 (HL 3/4 and decimal).

How do we count fractions and decimal numbers?

When we are working with whole numbers, it is easy to see what number comes next. We know that 743 is the next whole number after 742.

When counting fractions or decimal numbers, it is not predictable When counting fractions or decimal numbers, it is not predictable. We are not sure what comes after any fraction or decimal number.

It could be many different things, for example, quarters or eighths or halves. If you’re counting by quarters, 2 quarters comes next. If you’re counting by 8ths, 3/8 comes next. If you’re counting by halves, 1/2 comes next.

The same applies to decimal numbers The same applies to decimal numbers. The next number could be many different numbers.

For instance, any of these numbers could come next, depending on what you are counting by.

Notice that one way to make counting predictable is to count by the same amount.

If we choose quarters, we count by quarters…. one quarter If we choose quarters, we count by quarters…. one quarter...two quarters… three quarters… and so on.

Or if we are using decimal numbers and counting by quarters, we add 25 hundredths each time. We would count 25 hundredths… 50 hundredths… 75 hundredths… and so on.

In this way, we can count forever by whatever fraction or decimal number we choose.