Question

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

Answer 1

Answer:  $6 \frac{31}{33}$

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

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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 $6 \frac{x}{33}$ 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 $6 \frac{31}{33} = 6.\overline{93} = 6.93939393...$

Answer 2

Answer:

$6\frac{93}{100} = \frac{693}{100}$

Step-by-step explanation:

1. Turn 6.93 into a fraction: $6\frac{93}{100}$  
2. To turn into a mixed number, first multiply 6 and 100, then add 93. Put 693 over 100: $\frac{693}{100}$  

I hope this helps!