♻️Fractions ↔ Decimals ↔ Percents

Half a cake can be called one half, 0.5 of a cake, or 50% of it. Three names, one amount. Fractions and percents each have a home field, but a strong calculator switches between them freely — wearing whichever outfit makes the job easiest.

One number, three names

Let the most frequent guest step on stage first:

$\frac{1}{4} = 0.25 = 25\%$

One amount, three spellings: fractions explain "so many parts out of so many", decimals are good at adding and ordering, percents make comparisons instant. These are not three different numbers — just three outfits for one number.

Three conversion lanes

Conversion only ever takes one step, and there are just three lanes:

• Fraction → decimal: do the division, $\frac{3}{4} = 3 \div 4 = 0.75$;
• Decimal → percent: move the point two places right and add %, $0.75 = 75\%$;
• Percent → fraction: write it over one hundred, then simplify, $40\% = \frac{40}{100} = \frac{2}{5}$.

Discount %37

37% = 37/100 = 0.37 = 37/100

Drag the percentage in the grid and watch the three readouts below — however the outfit changes, they keep pointing at the same amount.

The pocket table

These conversions show up constantly, so they are worth memorizing:

Fraction	$\frac{1}{2}$	$\frac{1}{4}$	$\frac{3}{4}$	$\frac{1}{5}$	$\frac{1}{10}$
Decimal	0.5	0.25	0.75	0.2	0.1
Percent	50%	25%	75%	20%	10%

Know this little table by heart and you save half your time before the pencil even moves.

When the division never ends

Dividing out $\frac{1}{3}$ gives $0.333\ldots$ — the 3 never stops. A decimal like this is called a repeating decimal. The honest way to write it is $\frac{1}{3} = 0.333\ldots \approx 33.3\%$, with the approximation sign saying "rounded off here". Do not quietly swap the ≈ for an =, and do not chop it to 0.3 and hand it in — the lesson on estimation cares a lot about these near misses.

Which outfit for which job

• Comparing "which is more": percents win — 85% beats 0.8 at a glance;
• Adding, subtracting, multiplying: switch to a fraction or decimal first;
• Describing "parts of a whole": fractions carry the picture.

Check yourself

✅

Quick quiz

↺ Try again

1. 1. What is 0.6 as a fraction in lowest terms?

   3/56/102/3

2. 2. What is 3/4 as a percent?

   34%43%75%

3. 3. Which statement is written honestly?

   1/3 = 33.3%1/3 ≈ 33.3%1/3 = 3.3%