Albert Teen YOU ARE LEARNING:  Ordering Different Types of Numbers  # Ordering Different Types of Numbers ### Ordering Different Types of Numbers

Positive and negative integers, fractions and decimals are all different types of numbers. They can be compared and ordered in size.

1

Different types of number suit different purposes.

When measuring we often use decimals, when counting we use whole numbers (also known as integers).

2

Which four options below are types of numbers?  3

Which number in the image is a whole number?  4

Which number in the image is a decimal?  5

What type of number is $\dfrac{1}{4}$?  6

Our final number is $76\%$.

This is a percentage which can also be represented as a decimal, $0.76$. 1

Fractions and decimals fit in between integers

Since fractions and decimals aren't whole numbers, they go in the spaces between the integers on a number line. 1

$0.4$ and $4.854$ are both examples of decimals

They include a decimal point, where the numbers after the decimal point are the parts of a whole.

2

Like integer place value, each digit in a decimal has a unique decimal place value, which describes its size.

The first digit is called the tenths. 3

What does 4 represent in the number here? Tenths, hundredths, thousandths or ten thousandths?  Let's put these numbers in ascending order

1  2

To find the smallest number, put them in a column.

Make sure to line up the decimal point. 3

Which is the smallest number of the three?  4

We now need to find the smaller of the two remaining numbers. Which is it?  5

Now we can put the numbers in ascending order.

You can write them on one line now if you prefer. Which of the following two decimal numbers is the largest? A quick test! Which of the following decimals is largest? 1

How do we know which is larger between a decimal and a fraction?

Let's find out which of these is larger. 2

We need to convert the fraction to a decimal. What is $\dfrac{2}{5}$ as a decimal?  3

It is now easier to compare $0.4$ with $0.36$. How many tenths are there in $0.4$?  4

How many tenths are there in $0.36$?

$0.36$ is "3 tenths + 6 hundredths" so there are 3 tenths. 5

Now we know that $0.36$ has three tenths and $0.4$ has four tenths, which number is larger?  6

We have found the larger number between $\dfrac{2}{5}$ and $0.36$.

The larger number is $\dfrac{2}{5}$. 1

Let's try something a little harder.

Put these numbers in descending order. 2

What does the word 'descending' mean?  3

Next, we need to convert all the numbers to decimals. What is $76\%$ as a decimal?  4

What is $\dfrac{3}{4}$ as a decimal?  5

We now have four decimals and can compare the numbers as before.

Put the decimals in a column, making sure to line up the decimal point. 6

Which is the largest number?  7

What is the next largest number?  8

We now only have two numbers left.

The larger of these two is $0.706$. 9

We can now write our numbers in descending order

It's a good idea to double check our working. Let's put positive and negative numbers in ascending order: $0$, $-6$, $4.8$, $-6.3$

1

For ascending order do we start with the lowest or highest number? 2

What is the lowest number here? 3

As we move right from $-6.3$ on the number line what is the next smallest number? 4

We have our first two numbers, $-6.3$, $-6$. What number comes next? 5

Thats leaves us with the highest number

The highest number is $4.8$

6

The numbers in ascending order are $-6.3$, $-6$, $0$, $4.8$

When ordering negative and positive numbers in ascending order, work with the negative numbers first, then zero if it is included and finally the positive numbers.

1

Summary! We have looked at four different types of number:

Whole number (integer), for example $120$ Fraction, for example $\dfrac{1}{4}$ Decimal, for example $2.54$ Percentage, for example $76\%$ 2

The definition of:

3

To order decimal numbers, write them in a column and line up the decimal point.

Compare the tenths column first, then the hundredths and so on.

4

To order different numbers, convert the fractions to decimals

Compare them by lining up the decimal point.

5

Finally, we looked at negative numbers.

When putting numbers in ascending order, the negative numbers will all be on the left side.