Smartigo › Notes

Percentages in everyday life: discounts, tips and sales tax in your head

October 8, 2026 · 5 min read

"30 percent off everything." Lovely. But what does the jacket cost now? Most people guess a bit, nod, and trust the price tag. Yet nearly everything in daily life needs just two steps: find ten percent, then multiply or halve.

The ten percent trick

You get ten percent of a number by moving the decimal point one place to the left. 10% of $89 is $8.90. 10% of 240 is 24. Anyone can do that, and everything else builds on it.

• 20% is double that.
• 30% is three times.
• 5% is half.
• 15% is 10% plus 5%.
• 25% is a quarter, so halve twice.
• 1% you get by moving the point one place further.

The $89 jacket with 30 percent off: 8.90 times 3 is 26.70. So you pay 89 minus 26.70, roughly $62. In your head you round the price to 90 first and say: 27 off, about 63. That's enough to decide whether you want it.

Tipping

Bill of $46, you want to leave roughly ten percent: $4.60, rounded up to 5. Want 20 percent: double it, $9.20, so 9. Precision doesn't matter with tips. What matters is that you have an honest ballpark in three seconds.

Sales tax: add it in your head

Say the tax is 8 percent on a $50 item. 10% is 5, 1% is 0.50, so 8% is 5 minus two times 0.50: $4. In general, split an awkward rate into a round one and a small correction: 19% becomes 20% minus 1%, 7% becomes 10% minus 3 times 1%. For a price of $80 at 20 percent, the tax is $16, and the total $96.

Going backwards is nastier. If the sticker says $119 including a 19 percent tax, the price before tax is not 119 minus 19 percent but $100, because the 19 percent was taken on the base price. Rule of thumb: divide the total by 1.19, or in general by 1 plus the rate. If you want to memorise one thing, memorise this.

The trap: 20 up, 20 down

A price of $100 goes up 20 percent to $120. Then it drops 20 percent. Back to $100? No: 20% of 120 is 24, so $96. Percentages always refer to the value that's there right now. That's why "first 50 percent more, then 50 percent less" is a loss of a quarter. You see this pattern in every promotion where a price is "first raised, then reduced". It doesn't have to be malicious. You should just know how it works.

Percent or percentage points?

Interest rates go from 2 to 3 percent. That's one percentage point, but 50 percent more. Both statements are true. Which one ends up in the headline decides how dramatic it sounds. If you ask next time whether a report talks about points or percent, you've done more than most people.

Four problems

1. A sweater costs $45, 20 percent off. What do you pay?
2. A repair costs $60 before tax, and tax is 19 percent. Roughly how much tax?
3. A price rises 10 percent and then falls 10 percent. Is it afterwards higher, lower or the same?
4. A coat is $38 minus 25 percent. What's left?

When it matters

With a sweater, a dollar doesn't matter. With loans, rent increases and service charges it does. There, your feel for percentages decides whether you question something or wave it through. That's also a kind of suspicion with a method: people who calculate along get steamrolled less often.

For more on routes that are shorter in your head, see Mental math for adults.

Comparing prices: what does it cost per unit?

A second area where a feel for percentages and estimation meet is price comparison. The big pack costs $3.79 for 750 grams, the small one $2.29 for 400 grams. Which is cheaper? Don't work with crumbs, work with round numbers: the small one is about $2.30 for 400 grams, so roughly 58 cents per 100 grams. The big one is $3.80 for 750, roughly 50 cents per 100 grams. The big one wins by a few cents per 100 grams, and that's what counts.

What matters is that you never have to calculate against something the packaging wants to sell you as a discount. "20 percent more content" is not the same as "20 percent cheaper". At the same price, 20 percent more content is a reduction of about 17 percent per unit, because 100 divided by 120 is roughly 0.83. That's still a good deal. But it's not a fifth.

Once you've gotten used to this, you see packages differently. The advertising stays the same. Only your view of it changes.

Quick questions

How do I work out sales tax in my head?

Split the rate into a round part and a correction. For 19 percent: take 20 percent (two times ten percent) and subtract 1 percent. On $50: 10 plus 0.50 less, so $9.50.

How do I get from the gross price to the net price?

Divide by 1 plus the rate. As a rough check: $119 including 19 percent tax is $100 before tax, and $59.50 is about $50.