how do you convert a fraction into a decimal?

Question

i don't know how to convert. ex: 5/8 into a decimal

Answer 1

You just have to remember TIBO: top inside, bottom outside. The number on top of your fraction will go inside your division house and the bottom number of your fraction goes on the outside.

 

Your fraction 5/8 would be divided like this: 8⟩¯5. Your answer will be .625.

Answer 2

Divide 5 by 8 which equals .625. This is the decimal answer. 

Answer 3

divide 8 into 5.000...

divide until the division stops or until you see a digit or a group of digits repeat

divide 8 into 50 and get 6

8x6=48

50-48=2

bring down a zero and divide 8 into 20 and get 2

8x2=16

20-16=4

bring down a zero and divide 8 into 40 and get 5

8x5 =40

40-40=0, the division stopped or terminated and your answer is 0.625, a terminating decimal (don't forget that you must position the decimal point when dividing ! )

 

another solution:

5/8 is in lowest terms

factor 8 completely: 8=2x2x2 (write 8 as a product of prime factors)

notice that you have only 2's

if you factor the denominator and you get all 2's, all 5's, or a combination of 2's and 5's only, then the decimal expansion of the fraction will be terminating(don't forget to simplify the fraction first)

now write the fraction as an equal fraction whose denominator is a power of 10

note:when you factor the denominator, each 2 needs a 5 as a factor and each 5 needs a 2 as a factor to make a power of 10

example:100=2x2x5x5, 1000=2x2x2x5x5x5, 10,000=2x2x2x2x5x5x5x5, etc.(do you see a pattern ?)(the number of 0's equals the number of 2's and the number of 5's)

5/8=5/(2x2x2)

each 2 in the denominator needs to be multiplied by a 5, so the denominator must be multiplied by 5x5x5 or 125

therefore the numerator must be multiplied by the same number 125

5x125=625

the answer is 625/1000=0.625

another example: write 17/20 as a decimal

17/2x2x5

there are two 2's and one 5 so one of the 2's needs a 5 as a factor

multiply the denominator by 5 and multiply the numerator also by 5

(17x5)/(20x5)=85/100=0.85

another example: write 43/50 as a decimal

50=2x5x5

remember: each 2 needs a 5 and each 5 needs a 2

to get a power of 10 from 2x5x5 we multiply (2x5x5) by 2, and also multiply 43 by 2

(43x2)/(50x2)=86/100=0.86

 

Answer 4

 Very simply by performing the division: 

 

     1/ 4 means :

           split one unit into 4 equal parts

          Divide 1 over 4, divide 1 by 4 

          Divide 4 into 1

         They are all the same, that is why fraction sign ( /) is interchangeable with division sign (÷).

 

           Multiplication is repeated addition

           Division is repeated Multiplication. 

 

            _4__     When we divide 17 by 4, we want to know how many 4's we               4l  17              can subtract from 17, i.e.

             -16     If we split 17 candies between 4 kids, how many candies each                  1       get.

                   so, we take off 4 candies each time . Take 16 candies and we                            get one left 

 

                          if we want to split equally among kids. We cut it into 4 equal                             piece and give each kid one of the cut piece.

                            That cut piece is represented by 1/4, and read one forth.

                             This is called normal fraction.

                             17 ÷ 4 = 4  1/4 , which is 4 + 1/4 (1)

                             Now division and Multiplication are opposite of each other.

                               16 ÷ 4 = 4  ,  4*4 =16

                               17 ÷ 4 = 4  1/4   17 = 4*4 +1

                                 17 is called Dividend , 4 is called divisor, 4 quotient , 1 is remainder

                                  D(dividend) = d(divisor) * q( Quotient) + r ( Remainder)

                                 Equation (1) , can be written as:

                                    17/ 4 = 4 1/4                                  

                                Now conversion of 1/4 ( normal Fraction) to decimal fraction is by division:

 

                                0.25___  

                            4  l 10            We can not take 4 from 1 because 4 is less                                      -8           than 1, so we place

                                 20             a decimal point  to indicate the decimal                                           -20                fraction. and multiply  

                                  0            1 by 10 4 goes into 10, 2 times with                                                              remainder 2, then multiply        

                                               2 by 10, becomes 20, 20 goes into 4 5 times. 

                                    

       The idea behind converting normal fraction into decimal fraction, is the fact that our numbering system is decimal ( base ten), every digit shifted left its value increases 10 times number of shifts

  and shifted right its value decreases 10 times number of shifts.

     In Normal fraction 1/4, we divide unit into 4 equal parts.

      In decimal fraction we divide by 10, then subsequent remainders will be divided by 10 by number of 

      shifts, that is:( 100, 1000, 10000, .....)

       0.25 = 2* 1/10 + 5* 100    ( reads 25 hundredth = 25/ 100)

         25/100 = 1/4 if we divide numerator and denominator by 25.

    I know you asked a simple question and come out with this answer. But fractions are 3rd and 4th grade

     Math, that people come up to Algebra face a lot of problem. When ask a question then students just copy the answer without understanding the essence of the subject.