**Classify numbers** *KS3 Revision*

## 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.

**Question 2:** How many natural numbers are there in the following list?

-25 55 -13 0 2

-25 **55** -13 0 **24**

There are 2 natural numbers in this list.