# Question #92b0c

Mar 30, 2017

$4.70238095238 = \frac{395}{84}$

#### Explanation:

All graphing calculators and most scientific calculators should have a function that converts decimals to fractions.

TI-83(+) or TI-84(+)(CE):**
- Enter in the decimal $4.70238095238$
- Press [Math] -> [enter] (make sure you select "$\to \text{Frac}$")
- Press [enter]

Some other calculators have a button "F > < D"

Basic calculators which to not have a decimal to fraction function:
We are trying to find the denominator first, so the strategy is to multiply $4.70238095238$ by a number $y$ to get a whole number.
$\frac{x}{y} = 4.70238095238$
$x = 4.70238095238 \cdot y$

I tried multiple numbers for $y$, starting with $2$ and increasing, looking for $x$ value floats that are either repeating decimals or ones that I recognize. I stopped at $y = 7$ because then $x = 32.9166666$. Then I multiplied that by 3 because of the repeating 6 to get $98.75$. I finally multiplied by 4 to get
$x = 4.70238095238 \cdot \left(7 \cdot 3 \cdot 4\right) = 395$
$4.70238095238 = \frac{395}{84}$

*Note: I'm not super familiar with various types of calculators, so let me know if there's a different calculator function that I didn't mention