Here is a shop window with a big sale sign: 35% OFF. That little % symbol turns up everywhere: sale tags, phone batteries, test results, weather forecasts. Today we crack what a percentage really is, and how to write the very same amount as a fraction and as a decimal instead.

Have a think: if 35% of something is shaded, roughly how much of it is that? About a third? Less than half? Hold that estimate in your head, because we are about to check it three different ways.

35% as three forms

Watch the first battery, pinned at 35%. Say it with me: 35 out of 100, so the fraction is 35/100. Now look how it simplifies: both 35 and 100 divide by 5, giving 7/20. And as a decimal, 35 divided by 100 is 0.35. Same amount, three pictures.

Why dividing by 100 shifts two places

Here is the idea behind the decimals. Dividing by 10 makes every digit one column smaller: the 5 slides from ones into tenths. But 100 is ten tens, so dividing by 100 makes every digit two columns smaller. That is exactly why the point ends up two places along: 35 becomes 0.35, and 5 becomes 0.05. Two zeros in a hundred, two columns to move.

80% as three forms

Now look at the next battery, pinned at 80%. That is 80/100. Both numbers divide by 20, so it simplifies right down to 4/5. Notice how much smaller and tidier the fraction becomes. As a decimal, 80 divided by 100 is 0.80, which we write as 0.8.

12.5% as three forms (our stretch one)

Here is the tricky one, the stretch of the lesson. This is the only percentage today that is not a whole number, so do not worry if it feels harder than the pattern. Predict before the reveal: what tidy fraction do you think 12.5% makes?

After you predict, we will build the decimal and the simplified fraction together on the board. One note about the display: the battery can only show whole numbers, so it reads as roughly 13% on the screen, but the true value is 12.5%.

5% as three forms

Last one, pinned at 5%. That is 5/100, which divides by 5 to give 1/20. As a decimal, 5 divided by 100 is 0.05. Watch the point carefully here: the 5 sits in the hundredths column, so we need a zero holding the tenths place. This is the two-column shift again, 5 stepping two places down to 0.05.

Today we work through these percentages together, changing each into a fraction (in simplest form) and a decimal: 20%, then 40%, then 50%, then 75%. We build up: 20% starts us off, 40% is double it, 50% lands exactly on a half, and 75% is the three-quarters mark. Predict where the battery will sit before each reveal, then set the slider to each percentage and work out the simplified fraction and the decimal.

Today we match the battery to a target given as a percentage, a decimal or a fraction: first 50% (the half we already met), then 0.25, then the fraction 3/4, and finally 1/8. Each one asks you to recognise the same amount dressed differently, then set the slider to match and press Check.

One reminder for the last one: the battery only shows whole numbers, so it may round. If your setting is near the true value, you are right.