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Ordering Different Types of Numbers
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Ordering Different Types of Numbers

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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?

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You can select multiple answers

3

Which number in the image is a whole number?

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4

Which number in the image is a decimal?

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5

What type of number is 14\dfrac{1}{4}?

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6

Our final number is 76%76\%.

This is a percentage which can also be represented as a decimal, 0.760.76.

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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.

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1

0.40.4 and 4.8544.854 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.

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3

What does 4 represent in the number here? Tenths, hundredths, thousandths or ten thousandths?

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Let's put these numbers in ascending order

1

In ascending order, which number do we need to start with?

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2

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

Make sure to line up the decimal point.

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3

Which is the smallest number of the three?

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4

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

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5

Now we can put the numbers in ascending order.

You can write them on one line now if you prefer.

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Which of the following two decimal numbers is the largest?

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A quick test! Which of the following decimals is largest?

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1

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

Let's find out which of these is larger.

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2

We need to convert the fraction to a decimal. What is 25\dfrac{2}{5} as a decimal?

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3

It is now easier to compare 0.40.4 with 0.360.36. How many tenths are there in 0.40.4?

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4

How many tenths are there in 0.360.36?

0.360.36 is "3 tenths + 6 hundredths" so there are 3 tenths.

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5

Now we know that 0.360.36 has three tenths and 0.40.4 has four tenths, which number is larger?

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6

We have found the larger number between 25\dfrac{2}{5} and 0.360.36.

The larger number is 25\dfrac{2}{5}.

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1

Let's try something a little harder.

Put these numbers in descending order.

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2

What does the word 'descending' mean?

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3

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

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4

What is 34\dfrac{3}{4} as a decimal?

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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.

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6

Which is the largest number?

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7

What is the next largest number?

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8

We now only have two numbers left.

The larger of these two is 0.7060.706.

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9

We can now write our numbers in descending order

It's a good idea to double check our working.

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Let's put positive and negative numbers in ascending order: 00, 6-6, 4.84.8, 6.3-6.3

1

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

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2

What is the lowest number here?

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3

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

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4

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

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5

Thats leaves us with the highest number

The highest number is 4.84.8

6

The numbers in ascending order are 6.3-6.3, 6-6, 00, 4.84.8

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 120120 Fraction, for example 14\dfrac{1}{4} Decimal, for example 2.542.54 Percentage, for example 76%76\%

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2

The definition of:

Ascending - means going up, start with the smallest number Descending - means going down, start with the largest number

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.