answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
luda_lava
2 months ago
5

.580 80 repeating as fraction

Mathematics
2 answers:
zzz [12.3K]2 months ago
8 0

Response:

115/198

Detailed explanation:

Svet_ta [12.7K]2 months ago
4 0
To start, we will shift the non-repeating segment of the decimal to the left side by dividing by a power of 10.

Then we will assign a variable to represent the value and also shift the repeating segment to the left.

Essentially, the concept here is that we can denote the repeating portion with a variable, let's say "x", and move forward with the calculation;

\bf 0.580\overline{80}\implies \boxed{\cfrac{5.80\overline{80}}{10}}\qquad \textit{now, let's say }x= 5.80\overline{80}\\\\
-------------------------------

\bf thus\qquad \begin{array}{llll}
100\cdot x&=&580.80\overline{80}\\
&&575+5.80\overline{80}\\
&&575+x
\end{array}\qquad \implies 100x=575+x
\\\\\\
99x=575\implies x=\cfrac{575}{99}\qquad therefore\qquad \boxed{\cfrac{5.80\overline{80}}{10}}\implies \cfrac{\quad \frac{575}{99}\quad }{10}
\\\\\\
\cfrac{\quad \frac{575}{99}\quad }{\frac{10}{1}}\implies \cfrac{575}{99}\cdot \cfrac{1}{10}\implies \cfrac{575}{990}\implies \stackrel{simplified}{\cfrac{115}{198}}

you can verify that using your calculator.
You might be interested in
the vertex form of a function is g(x) = (x – 3)2 9. how does the graph of g(x) compare to the graph of the function f(x) = x2? g
Inessa [12570]
The vertex of the graph for the function g(x) = (x- 3)^2 + 9 is located 3 units to the right and 9 units upwards compared to the vertex of the function f(x) = x^2.
9 0
2 months ago
Read 2 more answers
Barry has 17 more than two-thirds of the number of cards in his brother’s baseball card collection. If x represents the number o
zzz [12365]

Answer: The precise answer is  2/3x + 17

Step-by-step explanation:

5 0
1 month ago
Read 2 more answers
The equation x2 – 1x – 90 = 0 has solutions {a, b}. What is a + b
PIT_PIT [12445]
X^2 - x - 90 =0
This quadratic equation is in the standard format ax^2+ bx + c
The total of the solutions can be found using -b/a (where a and b are the coefficients from the original equation, not the solutions)
The resulting answer is 1/1 = 1
8 0
1 month ago
Read 2 more answers
Other questions:
  • Norma Jean makes $25 per hour. She works 35 hours per week. She gets a commission of 15% on her total sales. How much should Nor
    5·2 answers
  • Match each type of function with a characteristic of its graph. Enter the letter of the correct characteristic next to the type
    16·2 answers
  • Which of the following values are in the range of the function graphed below? Check all that apply.
    13·2 answers
  • A sociologist is studying the social media habits of high school students in a school district. The sociologist wants to estimat
    7·1 answer
  • A straight rod has one end at the origin and the other end at the point (l,0) and a linear density given by λ=ax2, where a is a
    15·1 answer
  • Kirsten calculated the mean of 10 quiz scores. Later she was told there was an error in grading one of her quizzes. A quiz score
    11·2 answers
  • What is the sum of 14 and the opposite of 12
    7·1 answer
  • A lawn-mowing company is trying to grow its business. It had 30 clients when they started its business and wants to increase by
    10·1 answer
  • Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1?
    9·2 answers
  • Find the vertex, focus, directrix, and focal width of the parabola. <br><br> x2 = 20y
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!