Series and sequences

Find a fraction equivalent to the recurring decimal?

0.435643564356

Result

n =  44
d =  101

Solution:

a1=0.4356 q=0.0001 n=a1/(1−q) k=10000⋅ (1−q)=10000⋅ (1−0.0001)=9999 l=10000⋅ a1=10000⋅ 0.4356=4356 s=l/k=4356/9999≐44101≐0.4356 s=n/d=44/101 n=44a_{1}=0.4356 \ \\ q=0.0001 \ \\ n=a_{1}/(1-q) \ \\ k=10000 \cdot \ (1-q)=10000 \cdot \ (1-0.0001)=9999 \ \\ l=10000 \cdot \ a_{1}=10000 \cdot \ 0.4356=4356 \ \\ s=l/k=4356/9999 \doteq \dfrac{ 44 }{ 101 } \doteq 0.4356 \ \\ s=n/d=44/101 \ \\ n=44
d=101d=101

Try another example


Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





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




Tips to related online calculators
Need help calculate sum, simplify or multiply fractions? Try our fraction calculator.

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

Next similar math problems:

  1. Decimal to fraction
    fractions_2 Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.
  2. Fraction
    Gauss_stamp Fraction ? write as fraction a/b, a, b is integers numerator/denominator.
  3. 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.
  4. 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+....
  5. Sequence
    mandlebrot Find the common ratio of the sequence -3, -1.5, -0.75, -0.375, -0.1875. Ratio write as decimal number rounded to tenth.
  6. Six terms
    sequence_geo_3 Find the first six terms of the sequence a1 = -3, an = 2 * an-1
  7. Imaginary numbers
    Complex_conjugate_picture.svg Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is its sum?
  8. Geometric progression 2
    exp_x There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
  9. Tenth member
    10 Calculate the tenth member of geometric sequence when given: a1=1/2 and q=2
  10. GP members
    sequence_geo_8 The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?
  11. Five members
    pst3.JPG Write first 5 members geometric sequence and determine whether it is increasing or decreasing: a1 = 3 q = -2
  12. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  13. De Moivre's formula
    sqrt3_complex There are two distinct complex numbers z such that z3 is equal to 1 and z is not equal 1. Calculate the sum of these two numbers.
  14. A perineum
    sequence_geo_9 A perineum string is 10% shorter than its original string. The first string is 24, what is the 9th string or term?
  15. Geometric progression 4
    square_rot_1 8,4√2,4,2√2
  16. Five harvests
    zrno In the seed company, they know that, out of 100 grains of a new variety, they get an average of 2000 grains after harvest. Approximately how many grains do they get out of 100 grains after five harvests?
  17. GP - 8 items
    fn Determine the first eight members of a geometric progression if a9=512, q=2