1answer.
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
choli [55]
2 years ago
14

Which fraction represents the decimal 0. ModifyingAbove 1 2 with Bar? One-twelfth StartFraction 3 Over 25 EndFraction StartFract

ion 4 Over 33 EndFraction StartFraction 33 Over 4 EndFraction.
Mathematics
1 answer:
mestny [16]2 years ago
4 0

The considered decimal number is expressed by the fraction given by: Option C: 4/33

<h3>How to convert from decimal to fraction?</h3>

For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. Usually, to get the decimal of the form a.bcd, we count how many digits are there after the decimal point (if its finite), then we write 10 raised to that many power as denominator, and the considered number without any decimal point as numerator.

For example:

0.99 = \dfrac{99}{10^2} = \dfrac{99}{100}

(10 raised to power k = 1 followed by k zeroes)

<h3>What is the sum of an infinite geometric series?</h3>

The sum of an infinite geometric series having the initial term "a" and the multiplication per term is done by "r" such that r < 1

is given by

S_{\infty} = \dfrac{a}{1-r}

The series would look like a+ ar+ ar^2+\cdots

For the considered case, the given decimal number is

0.\overline{12} = 0.121212\cdots

We can check all the options available one by one, so as to know which one ends up giving this pattern, or we can use another technique as shown below.

0.12121...  = (0.1 + 0.001 + 0.00001 + ... ) + (0.02 + 0.0002 + 0.000002 + ... )

Each of the two series obtained are geometric series with the multiplication factor as 1/100

Using the sum formula for evaluation of an infinite geometric series, and the fact that initial term of first series is 0.1 and that of second series is 0.02, we get:
0.121212... = \dfrac{0.1}{1-1/100} + \dfrac{0.02}{1 - 1/100} = \dfrac{1}{99/100}(\dfrac{1}{10} + \dfrac{2}{100})\\0.121212...  = \dfrac{100}{99}\times(\dfrac{10}{100} + \dfrac{2}{100})\\\\\\0.121212 ... = \dfrac{12}{99} = \dfrac{4}{33}

Thus, the considered decimal number is expressed by the fraction given by: Option C: 4/33

Learn more about geometric series here:

brainly.com/question/16037289

You might be interested in
If an earthquake measures 10^4, what does it measure on the Richter scale?
devlian [24]
I think the answer is 4, the earthquake is a 4 in the scale.
6 0
3 years ago
The formula a=6s^2 will calculate the surface area of a cube. suppose you have a cube that has a surface area of 216 square inch
lawyer [7]
216 = 6s^2

can be solved in the following manner.

216/6=s^2
36 = s^2
sqrt(36) = s

flip for better overview

s = 6

the length of each side is 6 inches. :)
4 0
3 years ago
What is the gcf of 16 24 and 36
Nutka1998 [239]

Answer:

4

Step-by-step explanation:

Calculate Greatest Common Factor for :

   16, 24 and 36

Factorize of the above numbers :

   16 = 2^{4}  

   24 = 2^{3} • 3  

   36 = 2^{2} • 3^{2}  

Build a prime factors table

   Number of times each prime factor

   appears in the factorization of :

Prime  Factor     Number  16   Number  24   Number  36    G.C.F   (min)  

2 4 3 2 2

3 0 1 2 0

GCF = 2²

Greatest Common Factor is :

     4

Hope this helps :)

7 0
3 years ago
Can someone help me with this problem
chubhunter [2.5K]

n = 13\frac{1}{3}

This is found by dividing 32 by 2.4

4 0
3 years ago
Read 2 more answers
Please help me i’m doing an test
Ipatiy [6.2K]
The answer is c all the others are 1/3 fractions
3 0
3 years ago
Read 2 more answers
Other questions:
  • Is the underlined verb in the sentence regular or irregular? The Spanish photographer created a display of her photographs for t
    15·1 answer
  • the standard normal curve shown below models the population distribution of a random variable. What proportion of the values in
    13·1 answer
  • Find A ∩ B given A = {the Integers} and B = {the Rational numbers}.
    11·1 answer
  • Solve for x.<br> X^2-6x+10=2
    15·1 answer
  • in 1900, greenville had a population of 4000 people. Greenville's population increased by 100 people each year. Springfield had
    13·1 answer
  • In your own words, explain
    12·1 answer
  • 40% of what is = 400,000
    10·2 answers
  • Which of the following has a growth rate of 60%?<br><br> (no links please)
    11·1 answer
  • Does anyone know any good Algebra 1 studying tips. Big tests coming up.
    8·1 answer
  • ANSWER THE QUESTION FOR BRAINLIST !!
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!