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Here we will learn about decimals including how to add decimals, subtract decimals, multiply decimals and divide decimals.

There are also decimals worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you're still stuck.

What are decimals?

Decimals are numbers that have parts that are not whole. Our decimal system splits whole numbers into tenths, hundredths, thousandths, and so on.

If we have a number which has tenths, hundredths etc. we can place digits corresponding to those place values after a decimal point.

E.g.

For some fractions we can find an equivalent fraction with a denominator that is a power of ten.

E.g.

Ordering decimals

You will sometimes be required to compare the size of two decimal numbers or write a list of decimal numbers in order of size.

Ascending order means from smallest to largest while descending order means from largest to smallest.

Let's look at two techniques that can be used to help order decimals.

Extra zeros
Another helpful method is to write extra zeros on the end of the decimals so that all numbers have the same amount of decimal places. It can also aid comparison to write the numbers in a vertical line.

For example, which of the following numbers is the largest, 0.08, 0.4, 0.32?

Here we will put a zero on the end of 0.4 so that all the numbers have two decimal places and write them in a vertical line.

0.08

0.40

0.32

Looking down the column of the first decimal place we can see that 4 is the highest digit. Therefore 0.4 is the largest number on this list.

Compare each place value
It can be helpful to compare one decimal place at a time. This should be done starting with the tenths and grouping the numbers accordingly, before moving on to comparing the next decimal place.

For example, let's put the following numbers in ascending order: 0.5, 0.2, 0.25, 0.52, 0.05, 0.02, 0.052, 0.025, 0.205, 0.502

All of the numbers have zero units, so we will start by comparing the first decimal place and grouping the numbers accordingly.

Now within each group we will look at the subsequent decimal places to order them from smallest to largest.

So the final answer is: 0.02, 0.025, 0.05, 0.052, 0.2, 0.205, 0.25, 0.5, 0.502, 0.52.

Step-by-step guide: Decimal place value

Number line decimal

It can be helpful to visualise decimals on a number line. For example, this number line goes from zero to one in steps of 0.1.

You could be asked to mark a decimal number on a number line.
Here the number 0.472 has been marked. Its position has been estimated between 0.4 and 0.5, but closer to 0.5.

If we zoom in and consider a number line between 0.4 and 0.5 that goes up in steps on 0.01 then we can position the decimal 0.472 more accurately. This time the position has been estimated between 0.47 and 0.48, but closer to 0.47.

If we zoom in once more and consider a number line between 0.47 and 0.48 that goes up in steps on 0.001 then we can mark the decimal 0.472 in the exact position.

All the scales above were marked with ten intervals and therefore went up in steps of 0.1, 0.01 and 0.001. Some decimal scales have a different number of intervals and you may need to calculate the interval steps and mark the scale.

To calculate the length of an interval step we can use the formula:

(\text{Top of the scale} - \text{Bottom of the scale}) \div \text{Number of intervals}

Let's look at a few examples,
Example 1

This scale goes from 2 to 3 with 5 interval steps. We can use the formula to calculate the length of the interval steps.

(3 - 2) \div 5 = 0.2

So to mark each interval we add 0.2 each time starting with the number at the bottom of the scale; the number 2 in this case.

2+0.2 = 2.2

2.2+0.2=2.4

2.4+0.2=2.6

2.6+0.2=2.8

2.8+0.2= 3

Example 2

First we use the formula to find the length of the interval steps.

(13 - 9) \div 8 = 0.5

Then we can mark each interval by adding 0.5 each time starting with the number at the bottom of the scale.

Example 3

To calculate the interval steps we do (17 - 15) \div 5 = 0.4 Then we add 0.4 to 15 to mark the first interval and continue this process until we reach 17.

Step-by-step guide: Decimal number line

How to add decimals

E.g. Work out

1 Set up a column addition, writing one number above the other. Make sure the decimal points line up to ensure numbers in each column have the correct place value.

2 Add each column from right to left remembering to carry numbers to the next column when you get a two digit number.

3 Read off your answer, remembering to include the decimal point.

The answer is 13.48

How to subtract decimals

E.g. Work out

1 Set up a column subtraction, writing the larger number above the other. Make sure the decimal points line up to ensure numbers in each column have the correct place value. Fill in any gaps with zeros.

2 Subtract each column from right to left remembering to exchange (or borrow) from the left if required.

3 Read off your answer, remembering to include the decimal point. If the original subtraction would have given a negative answer, remember to include the negative sign.

The answer is 3.69

How to multiply decimals

E.g. Work out

1 Multiply any decimal numbers by an appropriate power of ten to make them whole numbers.

Multiply 5.3 by 10 to make it 53 and multiply 4.6 by 10 to make it 46.

2 Use column multiplication (or another preferred method) to find the product of the numbers.

3 Divide the product from Step 2 by the powers of ten used in Step 1. Check that the total number of decimal digits in the question is the same as the total number of decimal digits in the answer.

In Step 1 we multiplied 5.3 by 10 and 4.6 by 10.
10 × 10 = 100 so now divide by 100.

Check that the total number of decimals in the question matches the total number of decimals in the answer.

The answer is 24.38

How to divide decimals

E.g. Work out

1 If the divisor is already an integer, you can go straight to step 3. Otherwise, write the division as a fraction with the divisor as the denominator of the fraction.

2 Multiply both the numerator and denominator by the same power of 10 (or other appropriate value) to get an equivalent fraction with an integer denominator. (You can simplify the fraction further if possible to make the division easier to calculate.)

3 Use short division to calculate the answer to the original division problem. If the dividend is a decimal, line up the decimal point for your quotient answer and you may need to add some trailing zeros whilst doing the division to get the correct number of decimal places.)

The answer is 45.2

Decimals worksheet

Get your free Decimals worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Decimals worksheet

Get your free Decimals worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Practice decimals questions

Decimals GCSE questions

1. You are given that 156 \times 249=38844 .
Use this information to work out the following:

(a) 15.6 \times 2.49

(b) 0.156 \times 24.9

(c) 388.44 \div 2.49
(3 marks)

(a) 38.844
(1)
(b) 3.8844
(1)
(c) 156
(1)

2. (a) If F=ma , find F , when m=4.8 and a=1.75 .

(b) If D=\frac{t}{2}-g , find D , when t=6.5 and g=1.428
(4 marks)

(a) 4.8 \times 1.75
(1)
=8.4
(1)
(b) 6.5 \div 2 (=3.25)
(1)
Correct answer of 1.822
(1)

3. Below is the breakfast menu for a hotel.

The Smith family ordered one cooked buffet, one vegetarian buffet, three continentals, three teas and two coffees. Calculate their total bill.
(3 marks)

Calculating three teas (£ 3.60 ) or two coffees (£ 3.18 ) or three continentals (£ 14.25 )
(1)
Method to add cost of items
(1)
Correct total of £ 37.63
(1)

Learning checklist

You have now learned how to:

Understand and use place value for decimals, measures and integers of any size

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Still stuck?

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Free decimals revision guide for GCSE maths, including step by step examples, a free Decimals worksheet and exam questions.

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This will be a fabulous resource to brush up on the correct definitions of all things mathematics!

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Some cross curricular topics to consider if using Minecraft.

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Useful website for keeping up to date with science topics. Has some sections on misconceptions!

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Powering Up STEM with Minecraft

This week let's have a look at how we can use Minecraft: Education Edition to help children to develop STEM skills (Science, Technology, Engineering and Mathematics). By creating a common definition, it is important to first explain briefly what STEM learning is and why it is important.

"...STEM education aims to blend scientific inquiry and technological design processes through project based learning that focuses on developing students' critical thinking, problem solving, logical reasoning, technical, communication, collaboration, self-directing and creativity skills. STEM learning gives children opportunities to investigate an idea in different contexts and connect the learning across disciplines. Learning in this way becomes more relevant to students as they can draw learning points from their activities in different disciplines to construct meaning. " (Allsop, 2017).

This quote details what STEM learning is and how it relates to Computer Science. It also explains the main elements of STEM education. Developing STEM Skills: Ideas in Minecraft: Education Edition There are hundreds of fantastic Minecraft: Education Edition lesson plans available for educators to use in the classroom to support children developing their STEM skills. Providing children with opportunities to learn the same material in different contextual settings allows students to draw learning points from their activities in different disciplines and construct their own understanding and learning. Tackling Real-life Issues In Minecraft: Education Edition, students can create solutions for real-life problems. For example, students can design a dam (like in this image by Stephen Reid) to solve a water problem for a city or create a car to reduce the pollution in their local area. These lessons blend the concepts from science and engineering through design, tinkering and critical thinking. They might: * work with different materials * experiment with design ideas * use knowledge and skills from different disciplines such as using mathematics skill to decide the size of the dam for the population or science & math skills to think about wind power for their car design. Stephen Reid (@ ImmersiveMind) has additional projects on his website exploring solutions to many real-life problems using Minecraft: Education Edition.

Computational Thinking It is often said that computer science is the silent "C" in STEM. It has strong links with mathematics and science as well as design and technology. Minecraft: Education Edition provides opportunities for children to develop their CT approaches such as tinkering with ideas, persevering, creative thinking, working collaboratively, problem solving through design and creating but also computational concepts through Code Builder for Minecraft: Education Edition. Simon Johnson (@clcsimon) has developed quality activities for developing computational thinking skills using Code Builder. If you want to learn how to use MakeCode to create your own skyscrapers (like in this image by Simon Johnson) you can find the code here, and use it as an inspiration for your other creations.

Engineering with Bricks In Minecraft: Education Edition, students can experiment with levers, switches and electrical circuits just like in real life - or they can use the more accessible Minecraft tool, redstone. Using redstone, they can create farming systems that harvest themselves. Students can harness this energy to explore water cycles and renewable energy. They can even design an eco-system and delve into creative ways of storing energy. Additional engineering projects are supplied in the Minecraft: Education Edition website lessons area. Mathematical Thinking Minecraft: Education Edition enables a space for learners to visualize and investigate different objects and patterns from real life, which helps them to develop spatial thinking. Manipulating objects in a virtual world also empowers learners to test solutions for problems that they wouldn't be able to evaluate in real world. This process requires not only technical skills for using Minecraft but also critical thinking and logical reasoning for visualizing and predicting the outcomes of these solutions. It is important to give students the time and opportunities to discuss and explain their solutions, as this would allow them to make meaningful connections that would help them to further understanding. There are many more activities for developing mathematical thinking on the Minecraft: Education Edition website. Finally, one cannot expect children to develop their STEM skills without facilitating children's learning using appropriate teaching methods and tools. Teachers should provide opportunities for learners to work collaboratively, time to talk about their work, and space to express their ideas.

Learn More Allsop, Y. (2017) Computer Science: Silent C in STEM. in: Humble, S. Creating the Coding Generation in Primary Schools. London: Routledge. ------- Yasemin Allsop (@yallsop) worked as an ICT Coordinator in primary schools in London for almost 10 years. She is currently employed as a Lecturer in Primary Education at Institute of Education, University College London. Her research focus is children's thinking learning and metacognition when making digital games. She is the founder and co- editor of an online magazine called ICT in Practice where educators from around the world share their experiences of using technology in education. She is the co-editor of International Journal of Computer Science Education in Schools. She is also Code Week EU ambassador for the UK.

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Powering Up STEM with Minecraft | Minecraft Education Edition

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This week let's have a look at how we can use Minecraft: Education Edition to help children to develop STEM skills (Science, Technology, Engineering and Mathematics). By creating a common definition, it is important to first explain briefly what STEM learning is and why it is important.

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To help extend my poem knoweldge and nursery rhymes! Will be used in my current setting!

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Would you like to volunteer or find work in your local primary school? Are you thinking about becoming a teaching assistant, or becoming a teacher in the future? In this free course, Primary…

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