Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write the repeating decimal as a fraction.\newline.936936936.936936936

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Write a repeating decimal as a fractionright chevron icon

Full solution

Q. Write the repeating decimal as a fraction.\newline.936936936.936936936
  1. Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The digits 936936 are repeating.
  2. Express as xx: Express the repeating decimal as xx: x=0.936936936…x = 0.936936936\ldots
  3. Multiply by 10001000: To isolate the repeating pattern, multiply xx by 10001000 (since there are three digits in the repeating pattern): 1000x=936.936936…1000x = 936.936936\ldots
  4. Subtract Equations: Now subtract the original equation x=0.936936936…x = 0.936936936\ldots from the new equation 1000x=936.936936…1000x = 936.936936\ldots:1000x−x=936.936936…−0.936936936…1000x - x = 936.936936\ldots - 0.936936936\ldots
  5. Solve for x: Perform the subtraction: 999x=936999x = 936
  6. Find GCD: Now solve for xx by dividing both sides of the equation by 999999: x=936999x = \frac{936}{999}
  7. Simplify Fraction: Simplify the fraction by finding the greatest common divisor (GCD) of 936936 and 999999. The GCD of 936936 and 999999 is 99.
  8. Perform Division: Divide both the numerator and the denominator by the GCD to simplify the fraction: x=936/9999/9x = \frac{936 / 9}{999 / 9}
  9. Check Simplification: Perform the division: x=104111x = \frac{104}{111}
  10. Check Simplification: Perform the division: x=104111x = \frac{104}{111} Check the fraction to ensure it is fully simplified. Since there are no common factors between 104104 and 111111 other than 11, the fraction is in its simplest form.

More problems from Write a repeating decimal as a fraction

Question
Find the sum of the finite arithmetic series. ∑n=110(7n+4)\sum_{n=1}^{10} (7n+4)\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`
Get tutor helpright-arrow

Posted 1 month ago

Question
Type the missing number in this sequence: `2, 4 8`, ______,`32`
Get tutor helpright-arrow

Posted 2 months ago

Question
What kind of sequence is this? 2,10,50,250,…2, 10, 50, 250, \ldots Choices:Choices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the missing number in this pattern? 1,4,9,16,25,36,49,64,81,____1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_
Get tutor helpright-arrow

Posted 1 month ago

Question
Classify the series. ∑n=012(n+2)3 \sum_{n = 0}^{12} (n + 2)^3 \newlineChoices:\newline[A]arithmetic\text{[A]arithmetic}\newline[B]geometric\text{[B]geometric}\newline[C]both\text{[C]both}\newline[D]neither\text{[D]neither}
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the first three partial sums of the series.\newline1+6+11+16+21+26+⋯1 + 6 + 11 + 16 + 21 + 26 + \cdots\newlineWrite your answers as integers or fractions in simplest form.\newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the third partial sum of the series. \newline3+9+15+21+27+33+⋯3 + 9 + 15 + 21 + 27 + 33 + \cdots\newlineWrite your answer as an integer or a fraction in simplest form. \newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 1 month ago

Question
Find the first three partial sums of the series. \newline1+7+13+19+25+31+⋯1 + 7 + 13 + 19 + 25 + 31 + \cdots\newlineWrite your answers as integers or fractions in simplest form. \newlineS1=S_1 = ____\newlineS2=S_2 = ____\newlineS3=S_3 = ____
Get tutor helpright-arrow

Posted 2 months ago

Question
Does the infinite geometric series converge or diverge?\newline1+34+916+2764+⋯1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots\newlineChoices:\newline[A]converge\text{[A]converge}\newline[B]diverge\text{[B]diverge}
Get tutor helpright-arrow

Posted 1 month ago

View all (78)