Place value is the core building block of how maths works at KS2 level and far beyond. Put simply, a number’s place value tells you how large each digit of a number is along a horizontal scale. Digits further to the right have a smaller value than digits to the left.

Parents can use this guide to help explain the fundamentals of place value to their KS2-age children, starting with the basic place value headings of digits and decimals.

## 1. All numbers are made up of digits

There are only 10 digits:

**0 1 2 3 4 5 6 7 8 9 **

All numbers are formed using these digits.

e.g. **10 121 3,494 56,025 795,801 1,000,000 **

We refer to numbers as two-digit numbers and three-digit numbers and so on. E.g:

** 21, 485, 6947 **

These digit quantities can then be broken down into **place columns**: basic groupings starting with **units **(the numer one) and then expanding to **tens**, **hundreds, thousands **and so on.

For example, a two-digit number like 21 is made up of **2 tens **and **1 unit**.

A three-digit number like 485 is made up of **4 hundreds, 8 tens **and **5 units**.

A four-digit number like 6987, is made up of **6 thousands, 9 hundreds, 4 tens and 7 units. **

**Using digits to find the lowest and highest number in a range**

At KS2, pupils will need to know how to identify the biggest and the smallest numbers in a range. Digits and place value headings are the key to doing this.

First, search for the numbers with the fewest amount of digits. From these numbers, the one with the lowest first digit is the lowest number.

Let’s try out an example task. Establish the lowest number from this range:

**810, 62, 65, 108, 18, 381 **

1. Search for the numbers with the fewest digits:

**18, 62, 65 – these have two digits**

2. Search for the number with the lowest first digit:

**18 – The first digit of 18 is 1, which is lower than 6 (in both 62 and 65)**

Sometimes in these questions, you will have to choose between numbers with the same first digits. Let’s have a look an example.

This time, we’re going to find the highest number from the following range:

**811, 62, 65, 108, 18, 381, 817 **

1. First, search or the numbers with most digits:

**8108, 381, 811, 817 – **these all have three digits

2. Search for the numbers with the highest first digit:

**811, 817**

The first digits of these numbers is 8, which is higher than 1 (in 108) and higher than 3 (in 381).

3. We now have two numbers with identical hundreds and tens. This means we need to compare the units to find which is higher. 7 is higher than 1, meaning our answer is **817. **

**2. Ordering Numbers**

Once we have a working idea of the basics of place value, we can use it to carry out the basic KS2 maths task of putting numbers in order. Let’s try out a few examples.

1. Put these numbers in order from lowest to highest:

**37, 4897, 73, 987, 9874 **

Answer: **37, 73, 987, 4897, 9874**** **

2. Put these numbers in order from highest to lowest:

** 65, 62, 5634, 63, 3459, 3496**

Answer: **5634, 3496, 3459, 65, 63, 62 **** **

## 3. Understanding decimals

Decimal numbers are values that lie **in between whole numbers**. For instance, the number 3.5 is halfway between the whole numbers of 3 and 4.

These can be split up into columns of values just like whole numbers. The columns after the decimal point are called **decimal places**.

Let’s take the number 9.347

This number comprises **9 units**, **3 tenths**, **4 hundredths** and **7 thousandths**.

When ordering decimal numbers you should follow the same method you would with whole numbers. However, this time we are comparing the digits that sit **after** the decimal point.

It’s crucial to remember here that seeing more digits after the decimal point **does not mean the number is bigger**.

For instance, 0.45 is bigger than 0.382 because the digit in the **tenths**** column** (the first column after the decimal point) is bigger. 0.45 has 4 tenths, whereas 0.382 only has 3 tenths, so is smaller.

Let’s work through another example.

**Which decimal is larger: 0.43 or 0.403?**

1. We’ll start here by comparing the number in the **units column.**

0.43 and 0.403 both have 0 units.

2. Let’s now compare the digits in the **tenths column**.

0.43 and 0.403 both have 4 tenths.

3. Now lets compare the digits in the **hundredths column. **

0.43 has a 3 in this column.

0.403 has a 0 in this column, so is smaller.

We now have our answer: **0.43** is the larger decimal number.

You can use the < or > signs to show which number is bigger.

In this case, **0.43 > 0.403.**

## TuitionWorks is here to help your child conquer maths

I hope this article has helped you or your child get to grips with the concept of place value. But it can be hard to really master maths without practice and positive reinforcement.

If your child is still feeling less than confident about place value and other aspects of the Key Stage 2 maths curriculum, TuitionWorks can provide an intensive course of personalised, one-to-one maths lessons from a qualified teacher like me. Just get in touch for a free consultation.

### Andrew Hartshorn

Maths tutor at TuitionWorks

I have over twenty years’ experience of teaching both children and adults. I trained as a primary school teacher after a spending a number of years abroad teaching English as second language.

After qualifying with a PGCE in 2004, I attained my Masters Degree in Education. I believe in keeping my skills sharp and recently completed an online writing course with Harvard University.