Why 100 + 10% Gives 110, but 200 × 10% Gives 20

The same key, two behaviours

Type 100 + 10% into most calculators and you get 110. Type 200 × 10% and you get 20. Those look inconsistent, and in a strict mathematical sense they are — but the behaviour is deliberate, and once you see the rule it stops being surprising:

The rule: after + or −, the percent is read as a percentage of the number on the left. After × or ÷, it simply means divide by 100.

Why it was designed this way

Because it matches what people mean. “Add 10% tax to $100” is one of the most common calculations there is, and reading + 10% as “add 0.1” would make the key useless for it. Meanwhile “10% of 200” is naturally a multiplication, and there the literal reading is the right one.

This convention is often called Casio-style percentage, after the desktop and pocket calculators that standardised it. Most physical calculators, most phone calculators, and CalcBoard all follow it.

Where calculators disagree

Not everything follows the convention, which is why the same keystrokes can give different answers on different devices:

• Most physical and phone calculators: 100 + 10% = 110.
• Programming languages and spreadsheets: % is usually not a percent operator at all. In most languages it is the remainder operator, so 100 % 10 is 0. In a spreadsheet, =100+10% gives 100.1, because 10% is just the literal 0.1.
• Some scientific calculators require SHIFT+% or an explicit multiplication and behave differently again.

If a result surprises you, that difference is almost always the reason.

Checking which one you are using

Type 100 + 10%. If you get 110, your calculator uses the Casio convention. If you get 100.1, it is treating % as a plain divide-by-100.

The traps that follow

Increase then decrease does not return you home

100 + 20% is 120; 120 − 20% is 96. The second percentage is taken from the larger number. This is why a 50% loss requires a 100% gain to recover.

Discounts multiply, they do not add

30% off then a further 20% off is 0.7 × 0.8 = 0.56 — 44% off, not 50%. The discount calculator shows the working.

How CalcBoard handles it

CalcBoard implements the Casio convention exactly as tabulated above, and shows the full expression as you type so you can see what is about to be evaluated rather than discovering it afterwards. Percentages are computed in exact decimal, so a tax calculation on a long list of prices does not accumulate rounding error.

For rates you use repeatedly, named variables are usually clearer than the percent key: define tax=0.0825 once and write subtotal*tax, which is unambiguous on any calculator.

Frequently Asked Questions

Why does 100 + 10% equal 110 and not 100.1?

Because after a plus or minus, the percent key means 'that percentage of the number on the left'. So it adds 10% of 100. After × or ÷ the same key just divides by 100, which is why 200 × 10% is 20.

What is Casio-style percentage?

The convention where % is contextual: a percentage of the left operand after + or −, and a plain divide-by-100 after × or ÷. Most physical calculators, most phone calculators, and CalcBoard follow it.

Why does my spreadsheet give a different answer?

Spreadsheets treat 10% as the literal value 0.1, so =100+10% is 100.1. Most programming languages do not have a percent operator at all — % is usually remainder, so 100 % 10 is 0.

How do I add tax on a calculator?

Type the amount, then + , then the tax rate, then %. For 8.25% tax on $60: 60 + 8.25% = 64.95. Or multiply by 1.0825, which works on any calculator regardless of convention.

Does a percentage increase then decrease cancel out?

No. 100 + 20% is 120, and 120 − 20% is 96, because the second percentage is taken from the larger number.