Question

How do you convert 180° F to Celsius?

Answer 1

approximately `82.22^@C`

Explanation:

To convert from Fahrenheit to Celsius, use the formula:

`color(blue)(|bar(ul(color(white)(a/a)T_(@C)=(T_(@F)-32)xx5/9color(white)(a/a)|)))`

Substitute `T_(@F)` as `180` and solve for `T_(@C)`.

`T_(@C)=(T_(@F)-32)xx5/9`

`T_(@C)=(180-32)xx5/9`

`T_(@C)=148xx5/9`

`color(green)(|bar(ul(color(white)(a/a)T_(@C)~~82.22^@Ccolor(white)(a/a)|)))`

Answer 2

`180^@"F" = 82.bar(2)^@"C"`

Explanation:

The "standard" way of converting from Fahrenheit to Celsius is:

• Subtract `32`

• Multiply by `5/9`

So in our example:

`(180-32) * 5/9 = 148*5/9 = 740/9 = 82.bar(2)`

Conversely, to convert Celsius to Fahrenheit, reverse this process:

• Multiply by `9/5" "` (equivalent to dividing by `5/9`)

• Add `32`

So if we were starting with `82.bar(2)^@C`, we would find:

`(82.bar(2) * 9/5)+32 = (740/5)+32 = 148+32 = 180`

Alternatively, note that `-40^@F = -40^@C`, so we can convert from Fahrenheit to Celsius by the following steps:

• Add `40`

• Multiply by `5/9`

• Subtract `40`

Then we find:

`(180+40)*5/9-40 = 220*5/9-40 = 1100/9-40 = 122.bar(2)-40 = 82.bar(2)`

Similarly, we can convert Celsius to Fahrenheit by:

• Add `40`

• Multiply by `9/5`

• Subtract `40`

So:

`(82.bar(2)+40)*9/5-40 = 122.bar(2)*9/5-40 = 1100/5-40 = 220-40 = 180`