Question

Write 6.93 repeating a mixed number in simplest form.
6.93 =?

Answer 1

Answer:
`6 (31)/(33)`

This is a mixed number where the whole part is 6, and the fractional part is 31/33.

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Step-by-step explanation:

The 93 repeats forever, so we can say

x = 6.939393...

100x = 693.939393....

Subtracting the left hand sides leads to 100x-x = 99x

Subtracting the right hand sides leads to 693.939393.... - 6.939393... = 687

Notice how the decimal terms cancel out when we subtract.

We're left with 99x = 687 which solves to x = 687/99

This reduces to 229/33 when you divide both parts by 3.

The last step is to convert to a mixed number

The answer will be in the form
`6 (x)/(33)` where 6 is the whole part and x/33 is the fractional part. We know the whole part is 6 from the 6 in the original number given.

229/33 = 6.939393... helps confirm we're on the right track so far

this is another way of saying 229/33 = 6 remainder x, where x is the unknown remainder and the numerator we're after for the fraction x/33.

To get the remainder, we just compute 229-6*33 to get 31

This means 31/33 = 0.93939393...

and that
`6 (31)/(33) = 6.\overline{93} = 6.93939393...`

Answer 2

`6(93)/(100) = (693)/(100)`

Step-by-step explanation:

1. Turn 6.93 into a fraction:
   `6(93)/(100)`
2. To turn into a mixed number, first multiply 6 and 100, then add 93. Put 693 over 100:
   `(693)/(100)`

I hope this helps!