Fraction to a Percentage

[Debbie J]

When renaming the fraction 4/9 as a percentage, what is the answer? When I divide, I come up with a repeating decimal, and I don't know how to include this as part of the percentage. 44 and 4/9 %?

 

[mmm4444bot]

When I divide, I come up with a repeating decimal, and I don't know how to include this as part of the percentage.

If the exercise has no specific instructions about rounding or designating some specified number of decimal points, then I would guess that rounding to 44.4% is good enough.

Otherwise, a standard convention for indicating repeating decimals is to write a bar over the repeating part.

\(\displaystyle 44.\overline{4}\%\)


PS: Your word "percentage" above should be "percent". If you took (4/9)% of some number, it is the result that's called the percentage.

 

[soroban]

Hello, Debbie J!

When renaming the fraction 4/9 as a percent, what is the answer?
When I divide, I come up with a repeating decimal,
and I don't know how to include this as part of the percentage: 44 and 4/9 %.

It is also correct to write it as: \(\displaystyle 44\tfrac{4}{9}\%\)

 

[mmm4444bot]

Also (400/9)% :cool:

It would help to know the instructions.

 

[Debbie J]

If the exercise has no specific instructions about rounding or designating some specified number of decimal points, then I would guess that rounding to 44.4% is good enough.

Otherwise, a standard convention for indicating repeating decimals is to write a bar over the repeating part.

\(\displaystyle 44.\overline{4}\%\)


PS: Your word "percentage" above should be "percent". If you took (4/9)% of some number, it is the result that's called the percentage.

Thank you. I appreciate the help with the math and the vocabulary.

 

[HallsofIvy]

DebbieJ, note especially mmm4444bot's "If the exercise has no specific instructions about rounding or designating some specified number of decimal points" and "it would help to know the instructions". If you are doing this for schoolwork, ask your teacher exactly how he or she wants the answers written.

 

[Kaylaemarx]

Fraction to Percentage

The result is 44.44444444... but we can write it as 44.44 . Mathematics rule is that if the digit after point is more than 5 then we can round off the whole number to a number higher than what it is . Let us say, if the number would have been 44.666 then we could have written it as 45.0.

 

[HallsofIvy]

The result is 44.44444444... but we can write it as 44.44 .

No, we can't. Those are NOT the same number. If we wish to approximate to two decimal places we would get that. But why did you choose two decimal places rather than, say, three: 44.444?

Mathematics rule is that if the digit after point is more than 5 then we can round off the whole number to a number higher than what it is . Let us say, if the number would have been 44.666 then we could have written it as 45.0.

That is true when we are rounding to a specific decimal place. But why did you choose to round this to a whole number rather than the two decimal places you rounded to before- which would be 44.67?

The decision to round, and the choice of the decimal place to round to is far more important than a rule to round up or down.

(And, what you give is not the usual way to round. You say "if the digit after the point is more than 5 then we can round of the whole number to a number higher than it was" implying that if the digit is not more than 5 we round down- in particular, if it is equal to 5 to round down. Many texts instruct students that if that digit is 5 then you also round up. The reasoning is that the digits after that 5 mean the number is closer to the higher than the lower number. But others instruct us to always round to an odd digit. That is, if the number is 3.132225 we round down to 3.13222. If it were 3.12235 we would round up to 3.1224. The reasoning here is that '5' is halfway between 0 and 9 and this way, we will be rounding up half the time, rounding down half the time so any errors will cancel.)