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.\newline0.5515515510.551551551

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.\newline0.5515515510.551551551
  1. Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The repeating pattern is ＂551＂＂551＂.
  2. Convert to Fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as xx:x=0.551551551…x = 0.551551551\ldots
  3. Isolate Repeating Part: To isolate the repeating part, we multiply xx by 10001000 because there are three digits in the repeating pattern:\newline1000x=551.551551…1000x = 551.551551\ldots
  4. Subtract Decimal: Now, we subtract the original xx from 1000x1000x to get rid of the decimal part:\newline1000x−x=551.551551...−0.551551551...1000x - x = 551.551551... - 0.551551551...
  5. Solve for x: Perform the subtraction: 999x=551999x = 551
  6. Simplify Fraction: Now, we solve for xx by dividing both sides of the equation by 999999:x=551999x = \frac{551}{999}
  7. Simplify Fraction: Now, we solve for xx by dividing both sides of the equation by 999999:x=551999x = \frac{551}{999}We can simplify the fraction by looking for the greatest common divisor (GCD) of 551551 and 999999. The GCD of 551551 and 999999 is 11, so the fraction is already 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 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)