What is 1.04 repeating expressed as a ratio of two integers?

Question

Show your work.

              ——

What is 1.04 expressed as a ratio of 2 integers?

 

 

 

 

Answer 1

From the problem statement, it is not clear what the decimal value is because of the word "repeating."

 

If the value is 1.04444 (with the 4 repeating), then put the repeating part over repeating 999999 (9 repeating) and reduce it.  So,

    0.044444 / 0.99999 = 4/90

 

Remember the 1.0 and add it:    90/90  + 4/90   = 94/90  = 47/45

    47/45 = 1.044444 (4 repeating)

Answer 2

The simple way is to correlate it to something we're already familiar with:

1/9 = .111111.....

2/9 = .222222.....

4/9 = .444444.....

 

Sine we have a 0 in the tenths place, we need to add a correlating 0 to the denominator. Since the final answer is also a ratio, we need to convert the 1 into 90/90.

90/90 + 4/90 = 94/90

 

To show via division:

 

      1.044

   ----------

90|94.000

    -90

   -----

      40

       -0

    ------

        400

       -360
      ------

          400

         -360
       ------

            40

 

Answer 3

Working only (at the moment) with the repeating part:

 

n = 0.044...          multiply both sides by 10

10n = 0.44...        subtract top equation from bottom

9n = 0.4               divided both sides by 9

n = 0.4/9

n = 2/45

 

1. 044... = 1 + 2/45

1.044... = 47/45

Answer 4

Brianna, 1.04 = 104/100 

 

Reduce the fraction by dividing the numerator and denominator by 4. 104/4=26, 100/4=25. So the ratio is 26/25

Answer 5

SO my answer is 40?