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:

Convert the following repeating decimal to a fraction in simplest form. .5 bar(8) Answer:

Convert the following repeating decimal to a fraction in simplest form.\newline.58‾ .5 \overline{8} \newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Partial sums of geometric seriesright chevron icon

Full solution

Q. Convert the following repeating decimal to a fraction in simplest form.\newline.58‾ .5 \overline{8} \newlineAnswer:
  1. Set xx as decimal: Let xx be the repeating decimal 0.588‾0.58\overline{8}. We want to express xx as a fraction.\newlinex=0.588‾x = 0.58\overline{8}
  2. Multiply by 1010: To get rid of the repeating decimal, we multiply xx by a power of 1010 that shifts the decimal point to the right so that the repeating part lines up under the original decimal. Since there is one digit in the repeating sequence, we multiply by 1010.10x=5.888‾10x = 5.88\overline{8}
  3. Subtract to eliminate: Now we set up an equation to subtract the original xx from 10x10x to eliminate the repeating part.\newline10x−x=5.888‾−0.588‾10x - x = 5.88\overline{8} - 0.58\overline{8}
  4. Solve for x: Perform the subtraction on the left side of the equation. 10x−x=9x10x - x = 9x
  5. Express as fraction: Perform the subtraction on the right side of the equation, where the repeating decimals cancel each other out.\newline5.888‾−0.588‾=5.35.88\overline{8} - 0.58\overline{8} = 5.3
  6. Divide fraction: Now we have a simple equation to solve for xx.9x=5.39x = 5.3
  7. Find GCD: Divide both sides of the equation by 99 to solve for xx.\newlinex=5.39x = \frac{5.3}{9}
  8. Simplify fraction: Now we need to express 5.35.3 as a fraction. Since 5.35.3 is the same as 5310\frac{53}{10}, we can rewrite the equation.\newlinex=(5310)/9x = \left(\frac{53}{10}\right) / 9
  9. Simplify fraction: Now we need to express 5.35.3 as a fraction. Since 5.35.3 is the same as 5310\frac{53}{10}, we can rewrite the equation.\newlinex=(5310)/9x = \left(\frac{53}{10}\right) / 9 To divide a fraction by a whole number, we multiply the fraction by the reciprocal of the whole number.\newlinex=(5310)∗(19)x = \left(\frac{53}{10}\right) * \left(\frac{1}{9}\right)
  10. Simplify fraction: Now we need to express 5.35.3 as a fraction. Since 5.35.3 is the same as 5310\frac{53}{10}, we can rewrite the equation.\newlinex=(5310)/9x = \left(\frac{53}{10}\right) / 9 To divide a fraction by a whole number, we multiply the fraction by the reciprocal of the whole number.\newlinex=(5310)∗(19)x = \left(\frac{53}{10}\right) * \left(\frac{1}{9}\right) Now we multiply the numerators and the denominators.\newlinex=5390x = \frac{53}{90}
  11. Simplify fraction: Now we need to express 5.35.3 as a fraction. Since 5.35.3 is the same as 5310\frac{53}{10}, we can rewrite the equation.\newlinex=(5310)/9x = \left(\frac{53}{10}\right) / 9 To divide a fraction by a whole number, we multiply the fraction by the reciprocal of the whole number.\newlinex=(5310)∗(19)x = \left(\frac{53}{10}\right) * \left(\frac{1}{9}\right) Now we multiply the numerators and the denominators.\newlinex=5390x = \frac{53}{90} Finally, we simplify the fraction by finding the greatest common divisor (GCD) of 5353 and 9090, which is 11, so the fraction is already in simplest form.\newlinex=5390x = \frac{53}{90}

More problems from Partial sums of geometric series

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 9 months ago

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

Posted 5 months ago

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

Posted 5 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 5 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 7 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 5 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 7 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 7 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 9 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 5 months ago

View all (96)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant