A percent: a hundredth of the whole

One percent is one hundredth of the whole. Anyone who gets this has percentages in their pocket.

A percent is not magic. It is a hundredth.

Shop discounts, phone battery, election results — percentages everywhere. And the whole secret is: one percent is one hundredth of the whole.

The sign % is really a shortcut for “over a hundred”. So 25% = 25/100 = 0.25. There is nothing more in it.

Picture the whole as a chocolate bar broken into 100 equal pieces. One piece = 1%. Fifty pieces = 50% = a half. A hundred pieces = 100% = the whole bar. And 200% is two bars — percentages can happily grow past a hundred.

Important: a percent by itself weighs nothing. 50% of pocket money is a different amount than 50% of the price of a flat. A percent always belongs to some whole — and the first question in every problem is: of what is this calculated? That whole is called the base.

Jonáš reports at lunch: “I have only 20% left on my phone!” Sofie asks: “And that is how many hours?” Jonáš freezes. No idea. Sofie counts out loud: “The battery lasts about 10 hours in total. The whole is 10 hours, 20% is 20 hundredths of that. Ten hundredths would be an hour… so two hours.” Jonáš stares: “You took it through hundredths?” — “Sure. A percent is a hundredth of the whole. When you know the whole, you know everything.” Jonáš plugs in the charger. Two hours until the end of the film is not enough.

💡

Remember the anchors: 50% = a half, 25% = a quarter, 10% = a tenth, 1% = a hundredth. Most percentages in your head you can build from these four.

Three faces of the same number: percent, fraction, decimal

Every percent you can write in three ways and switch freely between them.

Percent → fraction: write the number over a hundred and simplify. 40% = 40/100 = 2/5.

Percent → decimal: divide by a hundred, so shift the decimal point two places left. 40% = 0.40 = 0.4. And 7% = 0.07 — watch that zero.

Decimal → percent: the other way, multiply by a hundred. 0.85 = 85%. The number 1.5 = 150%.

Fraction → percent: expand the fraction to denominator 100, or divide and then times a hundred. 3/4 = 75/100 = 75%. And 1/3 = 0.333… ≈ 33%.

Why three faces? Each is handy somewhere else. A fraction is best for a picture (a quarter of a pizza). A decimal for calculating with a calculator (× 0.25). A percent for talking to people (25% off).

The anchor table I want you to know by heart: 1% = 0.01 = 1/100; 10% = 0.1 = 1/10; 20% = 0.2 = 1/5; 25% = 0.25 = 1/4; 50% = 0.5 = 1/2; 75% = 0.75 = 3/4; 100% = 1 = the whole.

Convert 60% to a fraction in simplest form and to a decimal

Step 1: a percent means over a hundred: 60% = 60/100.

Step 2: I simplify. Sixty and a hundred I divide by twenty: 60/100 = 3/5.

Step 3: the decimal I get by dividing: 60 : 100 = 0.6. (Or by shifting the point in 60 two places left.)

Result: 60% = 3/5 = 0.6. Check through the anchors: 60% is more than a half (50%) and less than three quarters (75%). And 0.6 really sits between 0.5 and 0.75. That checks out.

There are 28 children in the class, 7 of them go to a club. What part of the class is that in percent?

Step 1: I write the part of the whole as a fraction: 7/28.

Step 2: I simplify by seven: 7/28 = 1/4.

Step 3: a quarter I know from the anchor table: 1/4 = 25%.

Result: 25% of the class go to the club. Without the anchor I would count 7 : 28 = 0.25 and times a hundred — same result, just slower. Anchors save time.

What does 150% of the original price mean?

Step 1: 150% = 150/100 = 1.5. So one and a half times.

Step 2: a thought with an example. A game cost 200 Kč. The new price is 150% of the original: 1.5 × 200 = 300 Kč.

Result: 150% means the whole and another half on top. Percentages over 100 are not a mistake — they say the new value is bigger than the original whole. When you see “a rise to 150%”, you know the price grew by a half.

⚠️

A percent without a whole means nothing. The sentence “I got 30% off” is useless until you know from what price. Always ask: of what? That whole (the base) is the most important word with percentages.

Play it

Before you go to the sheet, try it with your eyes. This is not a test — it is a game. Tap until you see it.

Practice: now you do it 🎲

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

Revise a fraction of a whole — percentages sit on that. Write only the number.

Practise the questions

On paper: a table of three faces

Draw a table with three columns: percent, fraction, decimal.

Fill the table rows for: 10%, 25%, 50%, 75%, 100%. Write fractions in simplest form.
Add harder rows: 5%, 12%, 150%. At 5% watch the zero in the decimal (0.05).
Colour a 10 × 10 square: 25 squares blue, 10 red. Write under it how many percent of the square each colour has and how much white is left.
Write three sentences from an ordinary day where a percent appears (battery, discount, a test), and for each say what the whole is.

Now you 💪

I can say in one sentence what a percent is: a hundredth of the whole.
I convert a percent to a fraction and a decimal and back.
In every sentence with a percent I can point to the whole it is calculated from.

✅

Done when: The table of three faces has all eight rows right, the square is coloured and it fits 25% + 10% + 65% = 100%.

What to take from this lesson

A percent = a hundredth of the whole. The sign % means over a hundred.
One number, three faces: 25% = 1/4 = 0.25.
Anchors by heart: 1%, 10%, 25%, 50%, 75%, 100%.
Percentages can go over 100 — then the value is bigger than the whole.
A percent without a whole (a base) says nothing. Always ask: of what?