Record of numbers in a format of a common fraction can be useful to representation of recurring decimal decimals in more compact and at the same time more exact, unreduced look. Such form of representation can be convenient in terms of convenience of placement on the paper or electronic page, for drawing up input data for various computing programs, etc.
Instruction
1. If it is necessary to present an integer in the form of a common fraction, then use unit as a denominator, and put a reference value in numerator. Such form of record of number will be called the improper common fraction as the module of its numerator is more than the denominator module. For example, number 74 can be written down as 74/1, and number-12 - as-12/1. If necessary you can increase numerator and a denominator in identical number of times - the value of fraction in this case will still correspond to initial number. For example, 74=74/1=222/3 or-12=-12/1=-84/7.
2. If the initial number is presented in a format of decimal fraction, then leave its whole part without changes, and replace a dividing comma with a gap. Put a fractional part in numerator, and as a denominator use ten built in degree with the indicator equal to the number of signs in a fractional part of initial number. The fractional part received as a result can be reduced, having divided numerator and a denominator into identical number. For example, to decimal fraction 7.625 there will correspond the common fraction 7 625/1000 which after reduction will accept value 7 5/8. Such form of record of a common fraction is called mixed. In need of it it is possible to lead to the wrong ordinary look, having increased the whole part by a denominator and having added result to numerator: 7.625 = 7 625/1000 = 7 5/8 = 61/8.
3. If the initial decimal decimal is recurring and periodic, then use, for example, the system of the equations for calculation of its equivalent in a format of a common fraction. Let's tell if the initial fraction is equal 3.5(3), then it is possible to make such identity: 100*x-10*x=100*3.5 (3)-10*3.5(3). It is possible to bring equality out of it 90*x=318, and it means that the required fraction will be equal 318/90 that after reduction will give the mixed common fraction 3 24/45.