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← Level 3 – Fraction kid

11 / 30 ⏱ 15 minutes

A fraction and a decimal number

Two write-ups of the same thing: how to convert between fractions and decimal numbers.

A half = 1/2 = 0.5

Half a litre of milk. On the carton it says 0.5 l. In a recipe 1/2 l. It is the same amount — just two different write-ups.

Fractions and decimal numbers are two languages for the same thing: parts of a whole. And you already know both! The last step left is learning to translate between them.

From a fraction to a decimal number there are two paths. The elegant one: expand the fraction into tenths or hundredths (1/2 = 5/10 = 0.5). The universal one: divide the numerator by the denominator (1 : 2 = 0.5) — division with a point from lesson five.

From a decimal number to a fraction it is even more direct: 0.7 = 7/10, because “zero point seven” literally MEANS seven tenths. Then just simplify if you need to.

A few conversions are worth knowing by heart like a times table: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/10 = 0.1. With them in your head you switch languages with no counting.

Filip and Ema compare discounts. One game has a discount “1/4 off the price”, the other “0.3 of the price”. “You cannot compare that, one is a fraction and the other… the other,” Filip frowns. Ema reaches for a translation: “A quarter is 0.25. I know that by heart — a quarter of a koruna is 25 hellers.” She writes 0.25 and 0.3 next to each other, pads to 0.30 and it is xong: 0.3 is the bigger discount. “I always convert both into the same language,” she shrugs. “Then it is ordinary comparing like in lesson two.”

💡

Money is your dictionary: a quarter of a koruna = 25 hellers = 0.25. A fifth of a koruna = 20 hellers = 0.2. Who knows coins knows conversions.

Translations both ways

Fraction → decimal number, path 1 (expanding):

Expand the fraction so the bottom is 10 or 100. Then you read it straight as a decimal number:

It works for denominators that can “grow” to 10 or 100: 2, 4, 5, 10, 20, 25, 50…

Fraction → decimal number, path 2 (dividing):

The fraction bar IS division: 3/4 = 3 : 4. Divide in writing with a point: 3 : 4 = 0.75. This path works always — even for ugly denominators.

Decimal number → fraction:

Read the number out loud and write what you hear: 0.7 = “seven tenths” = 7/10. 0.25 = “twenty-five hundredths” = 25/100. Then simplify: 25/100 = 1/4.

When is which language handy? Decimal numbers win with measuring and money (a calculator, price lists). Fractions win with splitting into parts (a third is ugly as a decimal number: 0.333…). Know both and switch by the situation.

Convert 3/5 to a decimal number

Path by expanding: I want 10 at the bottom. What times 5 gives 10? Two.

3/5 = 6/10 = 0.6.

Check by the dividing path: 3 : 5 = 0.6 (30 tenths : 5 = 6 tenths). Both paths met.

Picture it: 3/5 of a cake is more than a half — and 0.6 is also more than 0.5. The conversion did not change the size, only the write-up.

Convert 0.35 to a fraction in simplest form

Read: 0.35 = “thirty-five hundredths” = 35/100.

Simplify: 35 and 100 can both be divided by five: 35/100 = 7/20.

Once more by five? 7 and 20 have no common factor — xong, simplest form.

A check the other way: I expand 7/20 by five → 35/100 → 0.35 ✓. A translation there and back must return the original number.

Which is more: 2/5, or 0.45?

Two languages — I convert the fraction to a decimal number.

2/5 = 4/10 = 0.4.

I compare: 0.40 and 0.45. Wholes the same, tenths the same, hundredths 0 < 5.

0.45 > 2/5.

I could go the other way too: 0.45 = 45/100 = 9/20 and 2/5 = 8/20. Nine twentieths > eight twentieths — the same result, but more work. Always pick the easier direction of translation.

⚠️

1/4 is not 0.4. One divided by four is 0.25 — you cannot just copy the denominator after the point. Conversion is expanding to tenths/hundredths, or honest division. Who remembers coins (a quarter of a koruna = 25 hellers) will not make this mistake.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Bắt đầu with ten. When it goes well, add more.

Practise simplifying fractions — you need it all the time when converting from decimal numbers. Write the answer as a fraction with a slash, for example 3/4.

Practise the questions

On paper

Build your own translation dictionary — it will help you all year.

  1. Convert by expanding: 1/2, 3/4, 2/5, 7/10 and 9/20 to decimal numbers. Write the middle step with tenths or hundredths.

  2. Convert to fractions in simplest form: 0.5, 0.75, 0.2, 0.05 and 0.64.

  3. Compare (convert into one language): 3/4 and 0.7, then 0.5 and 3/5, then 1/4 and 0.25.

  4. Make a table-dictionary: in the left column the fractions 1/2, 1/4, 3/4, 1/5, 1/10, in the right their decimal outfits. Learn it by heart.

Now you 💪

  1. I can convert 3/5 to a decimal number by expanding and by dividing and I get the same.
  2. I can read 0.35 as “thirty-five hundredths” and write and simplify the fraction.
  3. I can pull from my sleeve: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75.
✅

Done when: You translate both ways between fractions and decimal numbers and you know the basic five conversions (1/2, 1/4, 3/4, 1/5, 1/10) by heart.

What to take from this lesson

© 2026 Ing. Martin Polak / AlgoRhino · Điều khoản sử dụng nội dung