Infinite decimal

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.

Result

x =  0

Solution:

a1=0.9 q=0.1 s=a1/(1q)=0.9/(10.1)=1 x=1s=11=0a_{1}=0.9 \ \\ q=0.1 \ \\ s=a_{1} / (1-q)=0.9 / (1-0.1)=1 \ \\ x=1-s=1-1=0



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. Series and sequences
    seq_sum Find a fraction equivalent to the recurring decimal? 0.435643564356
  3. Fraction
    Gauss_stamp Fraction ? write as fraction a/b, a, b is integers numerator/denominator.
  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. 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?
  7. Reduce to lowest terms
    fractions_16 Reduce to lowest terms : 32/124
  8. Package
    latky The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package?
  9. 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?
  10. Geometric progression 2
    exp_x There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
  11. Six terms
    sequence_geo_3 Find the first six terms of the sequence a1 = -3, an = 2 * an-1
  12. 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?
  13. Tenth member
    10 Calculate the tenth member of geometric sequence when given: a1=1/2 and q=2
  14. Geometric progression 4
    square_rot_1 8,4√2,4,2√2
  15. Geometric sequence 4
    Koch_Snowflake_Triangles It is given geometric sequence a3 = 7 and a12 = 3. Calculate s23 (= sum of the first 23 members of the sequence).
  16. Five members
    pst3.JPG Write first 5 members geometric sequence and determine whether it is increasing or decreasing: a1 = 3 q = -2
  17. GP - 8 items
    fn Determine the first eight members of a geometric progression if a9=512, q=2