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.801801801.801801801

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.801801801.801801801
  1. Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂801801＂ repeat indefinitely.
  2. Assign Variable xx: Let xx equal the repeating decimal: x=0.801801801…x = 0.801801801\ldots
  3. Multiply by 10001000: Multiply xx by 10001000 to shift the decimal point three places to the right, since the repeating pattern has three digits: 1000x=801.801801801…1000x = 801.801801801\ldots
  4. Subtract Equations: Subtract the original equation x=0.801801801...x = 0.801801801... from the new equation 1000x=801.801801801...1000x = 801.801801801... to eliminate the repeating decimals: 1000x−x=801.801801801...−0.801801801...1000x - x = 801.801801801... - 0.801801801...
  5. Perform Subtraction: Perform the subtraction: 999x=801999x = 801
  6. Divide by 999999: Divide both sides of the equation by 999999 to solve for xx: x=801999x = \frac{801}{999}
  7. Find GCD: Simplify the fraction by finding the greatest common divisor (GCD) of 801801 and 999999. The GCD of 801801 and 999999 is 99.
  8. Simplify Fraction: Divide both the numerator and the denominator by the GCD to simplify the fraction: x=8019/9999=89111x = \frac{801}{9} / \frac{999}{9} = \frac{89}{111}

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 3 months ago

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

Posted 2 months 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 2 months 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 2 months 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 2 months 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 2 months 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 3 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 2 months ago

View all (78)