Decimal to fraction

Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.

Result

A =  5183
B =  600

Solution:

8.638333333=AB  8.638333333=8.638+3104+3105+3106+....=  =86381000+3104111/10=  =86381000+3104109=  =86381000+310000109=  =86381000+39000=  =5183600  8.638333333=5183600  A=5183 B=600 8.638333333 = \dfrac{A}{B} \ \\ \ \\ 8.638333333 = 8.638 + 3 \cdot 10^{ -4}+ 3 \cdot 10^{ -5} + 3 \cdot 10^{ -6} + .... = \ \\ \ \\ = \dfrac{ 8638 }{ 1000 } + 3 \cdot 10^{ -4} \cdot \dfrac{1}{1-1/10} = \ \\ \ \\ = \dfrac{ 8638 }{ 1000 } + 3 \cdot 10^{ -4} \cdot \dfrac{10}{9} = \ \\ \ \\ = \dfrac{ 8638 }{ 1000 } + \dfrac{ 3 }{ 10000 } \cdot \dfrac{10}{9} = \ \\ \ \\ = \dfrac{ 8638 }{ 1000 } + \dfrac{ 3 }{ 9000 } = \ \\ \ \\ = \dfrac{ 5183 }{ 600 } \ \\ \ \\ 8.638333333 = \dfrac{ 5183 }{ 600 } \ \\ \ \\ A = 5183 \ \\ B = 600 \ \\







Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Following knowledge from mathematics are needed to solve this word math problem:

Need help calculate sum, simplify or multiply fractions? Try our fraction calculator.

Next similar math problems:

  1. Series and sequences
    seq_sum Find a fraction equivalent to the recurring decimal? 0.435643564356
  2. Infinite decimal
    series Imagine the infinite decimal number 0.99999999 .. ... ... ... That is a decimal and her endless serie of nines. Determine how much this number is less than the number 1. Thank you in advance.
  3. Fraction
    Gauss_stamp Fraction ? write as fraction a/b, a, b is integers numerator/denominator.
  4. Three glasses
    skleniceRGB Three glasses of different colors have different volumes. Red 1.5 liter is filled from 2/5, blue 3/4 liter is filled from 1/3, and the third green 1.2 liter is empty. Pour green glass 1/4 of the contents from the red glass and 2/5 of the content from the b
  5. Numbers division
    fractions With what number should be divided mixed number 2 3/4 to get 11/12?
  6. In center
    number_line What number lies in the center between a quarter of a fifth and a half of a third on the number axis?
  7. Barrel
    vino Barrel of wine is filled by 9/14. What part of the barrel will remain filled when 1/4 of the wine we pour from the barrel?
  8. Adding mixed 3
    mixed_fractions Why does 1 3/4 + 2 9/10 equal 4.65? How do you solve this?
  9. Infinite sum of areas
    height-of-equilateral-triangle Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tri
  10. Sum of series
    question Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+....
  11. Blueberries
    blueberry 5 children collect 4 liters of blueberries in 1.5 hours. a) How many minutes do 3 children take 2 liters of blueberries? b) How many liters of blueberries will be taken by 8 children in 3 hours?
  12. A baker
    pie A baker has 5 1/4 pies in her shop. She cut the pies in pieces that are each 1/8 of a whole pie. How many pieces of pie does she have?
  13. Two workers
    work One worker needs 40 hours to do a job, and the second would do it in 30 hours. They worked together for several hours, then the second was recalled, and the first completed the job itself in 5 hours. How many hours did they work together, and how much did.
  14. Discount and prices
    sale After a 29% discount, the new product price was € 426. What was the original price of the product?
  15. The sum 4
    clocks The sum of Robin's age is 45. Seven years ago, Robin was 16 years more than one half as old as Bruno then. How old is Bruno?
  16. Three-day trip
    cyclist The cyclist on three-day trip travel 30% of the total route on the first day, 3/5 of the rest on the second day and 35 km on the third day. How many kilometers did travel cyclists each day and how many?
  17. Video game
    time Nicole is playing a video game where each round lasts 7/12 of an hour. She has scheduled 3 3/4 hours to play the game. How many rounds can Nicole play?