# What is 1÷1π ? Is it (1÷1)π, is it 1÷(1π) or does it depend on the country?

Update:

The Huawei calculator in my phone gives π, and as Huawei is in China this might be a Chinese mathematical rule

The CALCU app in my phone gives 1÷π, and as CALCU is in the USA (as seen in the address of the app in Google Play) this might be an American mathematical rule

Do you know how it works in every country?

Relevance
• 1 ÷ 1π = (1 ÷ 1)π = 3.141592...

1 ÷ 1π = 1 ÷ (1π) = 0.318309...

• Unfortunately, it's ambiguous.

If you had written 1 ÷ 1 × π, then division and multiplication have the same precedence and you would perform them left to right.

(1 ÷ 1) × π

= 1 × π

= π

But yours is written as 1÷1π

Here some people see an implicit grouping of 1π, much like when you have a coefficient in front of a variable (e.g. 4x) and they might interpret it as 1 ÷ (1π)

= 1/π

When your expression seems ambiguous like this, I would recommend adding parentheses to explicitly show your intended grouping, rather than relying on others to apply the desired precedence rules.

Update:

The rules of precedence say the answer should be just π. If I type that into WolframAlpha, that's exactly what I get. But as you have shown, some calculator programs can get it wrong. For that reason, always use parentheses is you are worried it will be interpreted incorrectly.

I tried the CALCU app and it does seem to add some implied grouping.

If I type 1 ÷ 1 × π, the answer is π, but if I type 1 ÷ 1π, it see it as 1/π.

• Per the accepted order of operations, PE(MD)(AS), 1÷1π is equivalent to (1÷1)π = π

1÷1π is 1 divided by 1 multiplied by π

Since multiplication and division are equal priority, they are performed in strict left to right order. Therefore the first operation is 1 divided by 1 = 1. The result is multiplied by π yielding a result of π.

• one divided by 3.1415...

(1÷1)π would equal π