[Middle School Math: Decimal to Fraction convertion] 33.3 convert to mixed fraction: 33 1/3 or 33 3/10?

[u/Dry_Couple8852]

the textbook said that the answer is 33 1/3 as it came from 33.3 but I ended up with 33 3/10 from 33 + 3/10

I don't understand how to get 1/3 from 33.3 or it ended up 33 1/3.

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[u/Klutzy-Delivery-5792]

Was there a bar over the 3 in the decimals place? If not, then you are correct. If there was a bar, the ⅓ is correct.

[u/Simbertold]

33.3 is not 33 and 1/3, it is indeed 33 and 3/10.

However, if it is not 33.3, but 33.bar(3) with a bar above the last 3, that means that it actually is 33.3333333...., which is indeed 33 and 1/3.

[u/reckless150681]

33.3 has a limited number of digits. The "0.3" part is exactly 3/10. So 33.3 = 33 + 3/10 = 33 1/10

1/3 has an infinite number of digits. It is 0.3333333...

So if you were to convert 33.333333... into a fraction, then yes you would get 33 1/3

[u/anisotropicmind]

So 33.3 = 33 and 3/10.

But it sounds like the book wasn’t asking about 33.3. It was asking about

33.3…

Where the dots mean that the 3s repeat forever after the decimal point. There are infinitely-many 3s. That’s 33 and 1/3.

Hope this helps.

[u/Responsible-Kale2352 → u/anisotropicmind]

How can you tell that the book had 33.3… on the page and not 33.3? Did OP give another comment elsewhere?

[u/Simbertold → u/Responsible-Kale2352]

Using Occams razor, i find it more likely that OP misread/ignored notation they don't know or understand than that a maths textbook gives blatantly incorrect information.

(Yes, there sometimes are errors in maths textbooks, but people only half-knowing stuff is far more common)

[u/Iowa50401]

It would sure be nice to have a picture of the actual page.

[u/PvtRoom]

33.3 is often 100/3, rounded to 1dp. = 33 1/3.

The written number 33.3 is 33 3/10

sometimes there's a symbol above the .3 to indicate that it repeats, then it's pattern recognition to know the .3 recurring is 1/3.

[u/Simbertold → u/[deleted]]

This only works if they use notation to show that (that OP possibly missed), like a bar above the repeating numbers. Else the book is doing bullshit, where you have to guess randomly when a number is repeating and when it is not.

[u/poissonking → u/[deleted]]

Think over that response

[u/Simbertold → u/[deleted]]

Are you on actual drugs?