Decimal to Fraction Calculator

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

Show Instructions
  • In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`.
  • In general, you can skip parentheses, but be very careful: e^3x is `e^3x`, and e^(3x) is `e^(3x)`.
  • Also, be careful when you write fractions: 1/x^2 ln(x) is `1/x^2 ln(x)`, and 1/(x^2 ln(x)) is `1/(x^2 ln(x))`.
  • If you skip parentheses or a multiplication sign, type at least a whitespace, i.e. write sin x (or even better sin(x)) instead of sinx.
  • Sometimes I see expressions like tan^2xsec^3x: this will be parsed as `tan^(2*3)(x sec(x))`. To get `tan^2(x)sec^3(x)`, use parentheses: tan^2(x)sec^3(x).
  • Similarly, tanxsec^3x will be parsed as `tan(xsec^3(x))`. To get `tan(x)sec^3(x)`, use parentheses: tan(x)sec^3(x).
  • From the table below, you can notice that sech is not supported, but you can still enter it using the identity `sech(x)=1/cosh(x)`.
  • If you get an error, double check your expression, add parentheses and multiplication signs where needed, and consult the table below.
  • All suggestions and improvements are welcome. Please leave them in comments.
The following table contains the supported operations and functions:
TypeGet
Constants
ee
pi`pi`
ii (imaginary unit)
Operations
a+ba+b
a-ba-b
a*b`a*b`
a^b, a**b`a^b`
sqrt(x), x^(1/2)`sqrt(x)`
cbrt(x), x^(1/3)`root(3)(x)`
root(x,n), x^(1/n)`root(n)(x)`
x^(a/b)`x^(a/b)`
abs(x)`|x|`
Functions
e^x`e^x`
ln(x), log(x)ln(x)
ln(x)/ln(a)`log_a(x)`
Trigonometric Functions
sin(x)sin(x)
cos(x)cos(x)
tan(x)tan(x), tg(x)
cot(x)cot(x), ctg(x)
sec(x)sec(x)
csc(x)csc(x), cosec(x)
Inverse Trigonometric Functions
asin(x), arcsin(x), sin^-1(x)asin(x)
acos(x), arccos(x), cos^-1(x)acos(x)
atan(x), arctan(x), tan^-1(x)atan(x)
acot(x), arccot(x), cot^-1(x)acot(x)
asec(x), arcsec(x), sec^-1(x)asec(x)
acsc(x), arccsc(x), csc^-1(x)acsc(x)
Hyperbolic Functions
sinh(x)sinh(x)
cosh(x)cosh(x)
tanh(x)tanh(x)
coth(x)coth(x)
1/cosh(x)sech(x)
1/sinh(x)csch(x)
Inverse Hyperbolic Functions
asinh(x), arcsinh(x), sinh^-1(x)asinh(x)
acosh(x), arccosh(x), cosh^-1(x)acosh(x)
atanh(x), arctanh(x), tanh^-1(x)atanh(x)
acoth(x), arccoth(x), cot^-1(x)acoth(x)
acosh(1/x)asech(x)
asinh(1/x)acsch(x)

Enter a decimal or

Your input:

Write all suggestions in comments below.

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 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 a mixed number `1 (9)/(20)`

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)`