Decimals, Fractions and Percentages: Make the Connections

Fractions, decimals and percentages can express the same proportion in different forms. The key connection is hundredths: “per cent” means “per 100”, two decimal places show hundredths, and many fractions can be renamed with a denominator of 100. For example, 3/4 = 75/100 = 0.75 = 75%. The notation changes, but the value does not.

For Year 5, the goal is not to race through a conversion trick. It is to see why the forms match and choose a useful representation. England’s national curriculum asks pupils to read and write decimal numbers as fractions, understand percentages as parts per 100, and write percentages as fractions with denominator 100 and as decimals. Its non-statutory guidance describes percentages, decimals and fractions as different ways of expressing proportions.[1]

Contents

One value, three representations

Why hundredths make the connection visible

Worked example: convert three quarters

Worked example: convert seven twentieths

Start from a decimal or percentage

Use a number line as a check

Spot three common mix-ups

A short parent-led practice routine

Questions for explanation

Next step

One value, three representations

Suppose the same-sized whole is divided into 100 equal parts and 40 are selected.

As a fraction, this is 40/100, which can also be written as 2/5.

As a decimal, this is 0.40, or 0.4. The zero on the end does not change the value.

As a percentage, this is 40% because 40 of every 100 equal parts are selected.

So 2/5, 0.4 and 40% occupy the same point on a number line. They are not three answers; they are three names for one number.

This matters because each form can reveal something different. A fraction shows an exact relationship between a numerator and denominator. A decimal fits directly into our base-ten place-value system. A percentage fixes the comparison at 100. Flexible understanding means moving between them while keeping the quantity unchanged.

Why hundredths make the connection visible

A hundred-square, a strip divided into 100 equal sections or ten equal strips each split into tenths can show all three forms together. If 35 of the 100 parts are covered, the model represents:

35/100 = 0.35 = 35%

The Education Endowment Foundation says manipulatives and representations should be used purposefully to reveal mathematical structure, with explicit links between the materials and the mathematical ideas they represent. It also says they should support pupils towards independent mathematics rather than become a permanent prop.[2]

For this topic, the model has a precise job: it makes “out of 100” visible. Point to the same covered region while saying each name. Then remove the model and ask the child to recreate only the sketch they need.

A model is less helpful if the wholes change size. Half of a small strip and half of a large strip are the same proportion, but they are not the same physical amount. When comparing the written values, keep the reference whole consistent.

Worked example: convert three quarters

Convert 3/4 into a decimal and a percentage.

First, rename quarters as hundredths. To change 4 into 100, multiply by 25. Multiply the numerator by the same number so the fraction keeps its value:

3/4 = (3 × 25)/(4 × 25) = 75/100

Now read the hundredths in the other forms:

75/100 = 0.75 because 0.75 means 75 hundredths.

75/100 = 75% because 75% means 75 per 100.

Therefore:

3/4 = 0.75 = 75%

Check it against familiar benchmarks. Three quarters is greater than one half but less than one whole; both 0.75 and 75% sit in that interval.

Worked example: convert seven twentieths

Convert 7/20 into a decimal and a percentage.

Twentieths can be renamed as hundredths because 20 × 5 = 100. Apply the same factor to the numerator:

7/20 = (7 × 5)/(20 × 5) = 35/100

Read across from hundredths:

7/20 = 35/100 = 0.35 = 35%

A quick reasonableness check helps. Seven twentieths is less than one half because 7/20 < 10/20. The decimal 0.35 is less than 0.5, and 35% is less than 50%, so all three forms agree.

Not every denominator changes neatly to 100 using a whole-number multiplier. In Year 5 practice, begin with familiar fractions and denominators such as 2, 4, 5, 10, 20, 25, 50 and 100 so that the relationship remains visible. Do not turn the method into “add a percentage sign” or “move a decimal point” without explaining the value.

Start from a decimal or percentage

The connection works in every direction.

From a decimal

Convert 0.6 into a fraction and a percentage.

The 6 is in the tenths place, so:

0.6 = 6/10

Six tenths is equivalent to sixty hundredths:

6/10 = 60/100

Therefore:

0.6 = 6/10 = 3/5 = 60%

The decimal does not become 6%. The value 0.6 is six tenths, while 6% is six hundredths, or 0.06.

From a percentage

Convert 45% into a fraction and a decimal.

Start with the meaning of the symbol:

45% = 45/100

Forty-five hundredths written as a decimal is 0.45. The fraction can be simplified by dividing the numerator and denominator by 5:

45/100 = 9/20

Therefore:

45% = 0.45 = 9/20

Keeping 45/100 in the middle makes both connections visible before simplifying.

Use a number line as a check

The EEF identifies number lines as a particularly effective representation across Key Stages 2 and 3, while noting that how a representation is used matters.[2] A single line from 0 to 1 can hold fractions, decimals and percentages together.

Mark 0 at the left, 1 at the right and the halfway point in the middle. The halfway point can be labelled 1/2, 0.5 and 50%. Then place 1/4 = 0.25 = 25% halfway between 0 and 1/2, and 3/4 = 0.75 = 75% halfway between 1/2 and 1.

Use the line to test an answer rather than to decorate the page:

A value below 1/2 must also be below 0.5 and below 50%.

A value close to one whole should have a decimal close to 1 and a percentage close to 100%.

Equivalent forms should land on exactly the same point.

If they do not, revisit the conversion.

Spot three common mix-ups

Treating 0.4 as 4%

The decimal 0.4 means four tenths. Rename it as hundredths: 0.4 = 0.40 = 40/100 = 40%. By contrast, 4% = 4/100 = 0.04.

Reading the denominator as the percentage

For 3/5, 5 does not mean 5%. The denominator says the whole is split into five equal parts. Rename fifths as hundredths: 3/5 = 60/100 = 60%.

Changing the fraction’s value

Writing 7/20 = 7/100 changes the size of each part without changing how many parts are selected. If the denominator is multiplied by 5, the numerator must also be multiplied by 5: 7/20 = 35/100.

A short parent-led practice routine

Keep the session to one idea: naming the same proportion in different ways.

Build one benchmark. Draw a strip for 1/2 and connect it to 0.5 and 50%.

Use a denominator that scales to 100. Ask the child to show why 9/20 = 45/100 = 0.45 = 45%.

Reverse the direction. Start with 70% and ask for 70/100, 7/10 and 0.7.

Mix the cards. Write 3/5, 0.6 and 60% on separate cards and ask why they belong together.

Ask for a check. The child should place the forms approximately on a 0-to-1 number line and decide whether the position is sensible.

If an answer is wrong, ask “What does this form mean?” rather than supplying a rule immediately. “Per 100”, “tenths” and “equal parts” give you more useful information about the child’s understanding than a corrected symbol alone.

This home routine is an application of the mathematical ideas and representation principles in the sources; the EEF report is school-facing guidance and does not test this exact activity or a NeurofiED outcome.[2]

Questions for explanation

A secure connection can be explained in words, symbols and a simple model.

Why are 3/4, 0.75 and 75% equal?

How does 7/20 become a fraction with denominator 100?

Which is larger, 0.6 or 6%, and how do you know?

Why does adding a zero to make 0.4 = 0.40 leave the value unchanged?

Where would 35% sit on a number line from 0 to 1?

Can you match 13/20, 0.65 and 65%, then justify the match?

These questions focus on equivalent representations. Percentage word problems and fraction arithmetic are separate next steps.

Next step

Choose one fraction that can be renamed in hundredths. Ask your child to represent it as a fraction, decimal and percentage, then explain why all three forms belong at the same point on a number line.

Try a Maths lesson

Sources

[1] https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study — Department for Education, National curriculum in England: mathematics programmes of study.

[2] https://educationendowmentfoundation.org.uk/education-evidence/guidance-reports/maths-ks-2-3 — Education Endowment Foundation, Improving Mathematics in Key Stages 2 and 3.