Converting Fractions To Decimals And Decimals To Fractions: Fill & Download for Free

I have an unusual way of doing this, and it works like a charm.Let's take this decimal expansion:0.57541899441341… (continues…)Take the inverse:[math]\frac{1}{0.57541899441341}[/math] = 1.7378640776699Take off what's to the left of the decimal place (we'll keep that for later):0.7378640776699Take the inverse of that:[math]\frac{1}{0.7378640776699}[/math] = 1.3552631578947Take off what's to the left of the decimal, and invert it again:[math]\frac{1}{0.3552631578947}[/math] = 2.8148148148148Take off what's to the left of the decimal, and invert it again:[math]\frac{1}{0.8148148148148}[/math] = 1.227272727273Take off what's to the left of the decimal, and invert it again:[math]\frac{1}{0.227272727273}[/math] = 4.399999999999**Okay, here it's obvious that the correct answer rounds to 4.4, so we'll assume that. Take off what's to the left of the decimal point, and invert the rest:[math]\frac{1}{0.4}[/math] = 2.5Take off what's to the left of the decimal and invert what remains:[math]\frac{1}{0.5}[/math] = 2Alright!!! We've gotten to a whole number! Now we can work backwards from here to get the original fraction!This was the sequence of numbers we worked with earlier:1.73786407766991.35526315789472.81481481481481.2272727272734.42.52We'll start with 2 and work our way up. Take the inverse of 2 = [math]\frac{1}{2}[/math], and that's what the fraction is of the one above it (right of the decimal place), So it's 2[math]\frac{1}{2}[/math]. If we convert that to just fraction form it's [math]\frac{5}{2}[/math].To get the fraction to the right of the decimal of the one above that, we just invert it: [math]\frac{2}{5}[/math]. So the one above it ends up being [math]4\frac{2}{5}[/math], which converts to [math]\frac{22}{5}[/math].To get the fraction to the right of the decimal of the one above that, we invert it: [math]\frac{5}{22}[/math]. So that one ends up being [math]1\frac{5}{22}[/math], which converts to [math]\frac{27}{22}[/math].To get the fraction to the right of the decimal of the one above that, we invert it: [math]\frac{22}{27}[/math]. So that one ends up being [math]2\frac{22}{27}[/math], which converts to [math]\frac{76}{27}[/math].To get the fraction to the right of the decimal of the one above that, we invert it: [math]\frac{27}{76}[/math]. So that one ends up being [math]1\frac{27}{76}[/math], which converts to [math]\frac{103}{76}[/math].To get the fraction to the right of the decimal of the one above that, we invert it: [math]\frac{76}{103}[/math]. So that one ends up being [math]1\frac{76}{103}[/math], which converts to [math]\frac{179}{103}[/math].Almost there!!!Now we just invert that to get the original fraction:[math]\dfrac{103}{179}[/math]I've never seen a better way to convert from a complicated, incomplete decimal to a nice fraction.Edit:The reason why this works is because we are basically converting the decimal to continued fraction form, which can then easily be converted to fractional form.The continued fraction of the example we did above looks like this:[math]\frac{1}{1 + \frac{1}{1 + \frac{1}{2 + \frac{1}{1 + \frac{1}{4 + \frac{1}{2 + \frac{1}{2}}}}}}}[/math]which converts to [math]\frac{103}{179}[/math]

Conversion Of Decimals to Fraction:I recently learned about this and I thought I would share this with you all.To convert terminating decimals to fractions is relatively easy.For example:0.75 to fraction equals 75/1000.825 to fractions equals 825/10000.3 to fraction equals 3/10.But for non-terminating decimals.Example:How to convert 0.568945568945…… to fraction.How to convert 0.30253025…… to fraction.How to convert 0.45454545…. to frations.Actually to convert these types of fractions to decimals is also very easy.Let’s consider first example:0.568945568945…Did you see the pattern. 568945 is repeating .In these case, You put the repeating numbers to numerator.And There are 6 digits repeating continuously, So you divide by Six 9’s.568945/999999Again,0.30253025…In this case, 4 Digits are repeating, so3025/9999Again,0.454545…..Here, 45 is repeating.Thus,45/99.Now you need to convert into simpler fractions.Thanks.Edit: I would like to give in another example as well.What if we have repeating decimals after certain point.Example:0.657777..Here, its (657–65)/900.0.789676767..So, (78967–789)/ 99000Another,0.6789889898…So,(67898–67)/99900.Did you get the pattern?

5.36 in decimal is this in binary: 101.0101110000101000111101011100001010001111010111000010100011110101110000101000111101011100001010001111... (and it goes on and on)I use this decimal/binary converter because you can also convert fractions: Decimal/Binary Converter