## What you need to know

Things to remember:

• An integer is a positive or negative number that isn’t a fraction or a decimal.
• A whole number are non-negative integers (positive integer, including 0).
• A natural number is a whole number without 0.
• A square number is a number we get by multiplying a natural number by itself.
• Fractions and decimals are in none of these 4 categories

To classify numbers, we have to know 4 important terms:

Integers are positive or negative numbers that are neither fraction or decimals. For example, the following numbers are integers:

-123                 -56                   0                      49                    82

The following aren’t integers:

2.5                   56.46               13.55         $\frac{12}{7}$   $\frac{2}{3}$

Whole numbers are positive integers, including 0. For example, the following numbers are whole numbers:

0                      8                      12                    49                    294

The following aren’t whole numbers:

-245                 -123                 -56                   -13                   -5

Natural numbers are any whole numbers that aren’t 0. For example, the following numbers are natural numbers:

1                      12                    49                    98                    103

The following aren’t natural numbers:

-245                 -123                 -56                   -13                   0

Square numbers are found my multiplying two natural numbers together. For example, the following numbers on the right are square numbers:

$$1^2=1\times1=1$$

$$2^2=2\times2=4$$

$$3^2=3\times3=9$$

$$4^2=4\times4=16$$

$$5^2=5\times5=25$$

$$6^2=6\times6=36$$

$$7^2=7\times7=49$$

$$8^2=8\times8=64$$

$$9^2=9\times9=81$$

$$10^2=10\times10=100$$

$$11^2=11\times11=121$$

$$12^2=12\times12=144$$

The following wouldn’t be square numbers:

$$1.5^2=1.5\times1.5=2.25$$

$$3.8^2=3.8\times3.8=14.44$$

$$7.7^2=7.7\times7.7=59.29$$

Prime numbers are natural numbers that only have two factors. The following numbers are prime numbers:

2                      7                      11                    17                    29

The following aren’t prime numbers:

8                      27                    55                    84                    123

We can think of these classifications as being inside each other, like in a Venn diagram:

So, square numbers are a type of natural number; natural numbers are a type of whole number; and whole numbers are a type of integer. To classify numbers, we just need to put them in these groups. The strength of a classification depends on how specific you can be. So, classifying a number as a “prime number” is stronger/better than classifying it as just an “integer”, as it gives us more information. So, the smaller the group it is in, the better the classification!

How would we classify 49?

Well, if we look at our examples, 49 in each list, apart from

How would we classify -15?

Well, only the integers can be negative, so -15 must be an integer.

Find the odd one out in the following list:

6                      8                      -14                   2.4                   -6

All of these numbers are integers, apart from 2.4 which isn’t. 2.4 is the odd one out.

Which number has the strongest classification?

6                      -5                     5                      8                      0

Here, 5 has the strongest classification, because it is prime!

## Example Questions

#### Question 1:  What is the strongest way of classifying the number 9?

Is 9 an integer? Yes.

Is 9 a whole number? Yes

Is 9 a natural number? Yes

Is 9 a square number? Yes

Is 9 a prime number? No

The strongest way of classifying the number 9 is as a square number.