Decimal to Fraction Calculator

The calculator will convert decimal (simple, repeating or recurring) into fraction (and, if possible, into mixed number), with steps shown.

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Solution

Your input: convert `1.45` into fraction.

Recall that every mixed number/fraction consists of an integer part and a proper fraction. Also, a decimal consists of an integer and a decimal parts.

Mixed numbers and decimals are very similar: if they represent the same number, their integer parts are equal, and what we want is to convert the decimal part of the decimal into the fractional part of the mixed number.

Our decimal consists of the integer part `1` and the decimal part `0.45`.

So, we ignore the integer part and work with the decimal part `0.45`.

Recall that every number can be represented as a fraction with a denominator that equals `1`.

In our case, we can write that `0.45=(0.45)/1`

Since the decimal part contains 2 digits (to the right of the decimal point), we need to multiply our number by `10^(2)=100` to obtain an integer.

Now, using the equivalence of fractions, we can write that

`(0.45)/1=(0.45*color(red)(100))/(1*color(red)(100))=(45)/(100)`

Next, try to reduce the fraction.

Since the greatest common divisor of the numerator and the denominator equals `5`, we can write that `(45)/(100)=(9*color(red)(5))/(20*color(red)(5))=(9)/(20)`

And don't forget about the integer part.

Our decimal becomes `1 (9)/(20)` (mixed number).

The last thing is to convert the mixed number into an improper fraction:

`1 (9)/(20)=(1*color(red)(20))/(color(red)(20))+(9)/(20)=(1*20+9)/(20)=(29)/(20)`

Answer: `1.45=1 (9)/(20)= (29)/(20)`