Mathematics Middle School

Find the common fraction equivalent to 0.12


The 12 is repeating.

Please show all steps I have answer just can't figure out steps! Thanks!

Answers

Answer 1
The answer is:  " [tex] \frac{4}{33} [/tex] "  .
______________________________
Given:  0.1212121212..... repeating ;  write that value as a fraction;
______________________________________________________
In other words; we are given:  "0.1212121212..... repeating infinitely" ;  

→ that is to say; "0.12 ...  ;  {the "12" decimal portion repeats infinitely} ; 
_______________________________________________________
→ We write this value, as a fraction, as:  "12/99" ;
__________________________________________
→Explanation:
__________________________________________ 


Note:  "0.99999999...... repeating infinitely;  =  "1" .
_________________________________________
→Since:

Let us say that we have: 

"x = 0.999999 ; repeating infinitely;  

In order words, let us say we have: "x = 0.9.... ;  the "9" decimal repeats infinitely; 
_____________________________________________________
   Then "10x" ;  (that is: "10" multlipled by "x";  or "10*x" or "10x" );  is equal to:

"10" * (0.999999.....)  = 9.99999999...... (the "9" decimal repeats infinitely);

in other words:  10x = 9.99999999....

Divide each side by "10" ;

to get "x = 0.9999999....." ; the decimal "9" repeats indefinitely...." ;

But if you have:  "10x = 10" ;  divide each side of the equation by "10" ; 
   you get: "x = 1" . 
____________________
Also,  if "x = 0.9999...(repeating infinitely); 

then:  10x = 9.99999.
_______________________________________________
           10x  =  9.999999999999999......
       −     x  =  0.999999999999999.......
    _____________________________________
            9x  =  9.00000000000000000000.....

 →  9x = 9 ; 

Divide each side of the equation; to get; 

 9x /9 = 9/ 9 ;  to get:  x = 1 ; and we have: x = 0.9999.... ;  so
  x= 0.99999.... = 1 ; 
__________________________________________________
So, if the numbers "12" is repeating, we divie "12" by "99" ; 
  that is; we divide "12" by "two 9's" ;  since "12" is a "TWO-digit number"; a "two-digit number" is being repeated infinitely.
________________________________________
            So;  0.12121212.....(the "12" is the decimal that repeats infinitely);            
                   
=  12/99 ;  which can be simplified;

Divide each side (both the numerator AND the denominator); by "3" ;
_________________________________________
  " 12/99 "  =  "(12÷3) / (99÷3) = 4/33 " .
_________________________________________
The answer is:  [tex] \frac{4}{33} [/tex]  .
_________________________________________
Answer 2
answer is 4/33 hope this helps

Related Questions

In a class of 160 students, 90 are taking math, 78 are taking science, and 62 are taking both math and science. What is the probability of randomly choosing a student who is taking only math

Answers

The probability of choosing a student who is taking only math from a class of 160 students, with 90 taking math and 62 taking both math and science, is 0.175.

The question asks for the probability of randomly choosing a student who is taking only math in a class of 160 students, where 90 are taking math, 78 are taking science, and 62 are taking both math and science. To find the number of students taking only math, subtract the number of students taking both subjects from the total number taking math (90 - 62 = 28). The probability is then the number of students taking only math divided by the total number of students, which is 28/160.

The probability can be calculated as 28 divided by 160, or 0.175.

here are 96 girls in a junior class of 176 students. Find the ratio of girls to boys.

Answers

176 - 96= 80

Meaning there's 80 boy in the class.

The unsimplified version of the ratio would be 80:96 or 80/96 in fraction form

But if your looking for it simplified it would be 5:6 or 5/6 in fraction form.

Hope this helps :)

What is the probability that two events, A and B, will occur at the same time?

answer choices:
P(A or B)


P(A and B)


P(A)+P(B)

Answers

P (A and B) is the answer for this question, unless the question asks 'not the same time' Then your answer would be P(A or B).

Find the extraneous solution of the equation |2x−10|=−3x

Answers

|2x - 10| = -3x
Open absolute value symbol
2x - 10 = 3x
OR
2x - 10 = -3x

x = -10
OR
x = 2

Plug them in...
|2(-10) - 10| = -3(-10)
30 = 30
x = -10 is not the extraneous solution.

|2(2) - 10| = -3(2)
6 ≠ -6
x=2 is the extraneous solution.
Have an awesome day! :)
Final answer:

For the equation |2x−10|=−3x, the absolute value cannot be negative, therefore there is no valid solution. Any solution derived would be considered an extraneous solution. Extraneous solutions are those that appear during the solving process but are not valid.

Explanation:

The given equation is a mathematical expression |2x−10|=−3x. However, it should be noted that the absolute value of a number cannot be negative, so technically, there is no solution to this equation. This means the equation doesn't have a valid solution, but rather an extraneous solution.

An extraneous solution often arises in the process of solving an equation but is not a true solution. They often appear when you square both sides of an equation, as this often introduces new solutions that weren't part of the original equation.

So, in this case, since the absolute value can not be negative, it is impossible for |2x - 10| to be equal to -3x. Hence, any solution derived from this equation would be considered an extraneous solution.

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Bella uses 56 beats to create a necklace.she wants to make 23 necklaces for a craft show. unfortunately,she was 15 beads short and cannot finish the last necklace.how many beads did she start with?

Answers

To find how many she started with do 56 x 23 - 15

Graph y-5=-2/3(x+9)
50 points !!!

Answers

Here is the graph. A way you could graph this is notice how this equation is in point-slope form.

A line that passes through (x1, y1) and has slope m
y - y1 = m(x - x1)

Using the equation, you could find out that the line has a slope of -2/3 and passes through the point  (-9,5).

Have an awesome day!

Determine the amount potential energy of 5.0kg book that is moved to three different shelves on a bookcase. The height of each Shelf is 1.0 m, 1.5

Answers

p. e = mgh
m=5kg
g=10ms-²
h=1 + 1.5 + (you didn't specify the third shelf height) i assume it is 2m
so total = 1+1.5+2= 4.5
p. e = 5×10×4.5 = 225joules

solve each equation x-6=8

Answers

Equation is
x-6=8
x=8+6
x=14
X equal to 14

The solution to the equation  x - 6 = 8 is x equal to 14.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression x - 6 = 8.

Now, Separating the variable and constants by moving them to other sides

we have, x = 8 + 6.

x = 14.

Also moving terms to the other sides changes its sign.

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Sara is multiplying two factors,one with one decimal place and one with two decimal places.She says that the product could have two decimal places. is she correct?

Answers

She is incorrect, the product will have 3 decimal places.

Carmelo puts $2,200.00 into savings bonds that pay a simple interest rate of 3.4%. How much money will the bonds be worth at the end of 5.5 years?

Answers

Hello there! So, the first thing we do when solving these types of problems is to find the interest rate. Because this is simple interest, the amount earned will be constant. The formula for this is I = prt. The principle is the $2,200. The rate earned per year is 3.4%. 2,200 * 3.4% (0.034) is 74.80. That's $74.80 worth of interest each year. The amount of time is 5.5 years. 74.8 * 5.5 is 411.4. Carmelo will earn $411.40 worth of interest in 5.5 years. However, that's not all. We are looking for the total amount of his bonds, which means add the interest and his initial amount in the bank. 2,200.00 + 411.40 is 2,611.4. Carmelo's saving bonds will be worth $2,611.40 at the end of 5.5 years.

The bonds will be $2611.40 at the end of 5.5 years.

What is simple interest rate?

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

Simple interest rate formula

F.V = [tex]P.V (1+rt)[/tex]

F.V = Final value

P.V = Principal value

Given

Principal value P.V = $2200.00

Rate r = 3.4%

Time t = 5.5 years

Simple interest rate formula

F.V = [tex]P.V (1+rt)[/tex]

F.V = [tex]2200(1+3.4 \% \times 5.5)[/tex]

F.V = [tex]2200(1+0.034 \times 5.5)[/tex]

F.V = 2200 × 1.187

F.V  = 2611.40

Hence,

The bonds will be $2611.40 at the end of 5.5 years.

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A function is shown below:

f(x) = (0.07)x

What does the function represent?
A. Exponential growth of 7%
B. Exponential decay of 7%
C .Exponential growth of 93%
D. Exponential decay of 93%

Answers

the function represents an exponential decay of 93%, as the number will enormously decrease in 0.93.

Answer:

D. Exponential decay of 93%

Step-by-step explanation:

We are given an exponential function [tex]f(x) = (0.07)^x[/tex].

We know, the standard exponential function [tex]y= a(b)^x[/tex], where a is the initial value and b is growth factor.

If b is greater than 1, then it would be an Exponential growth and if  b is less  than 1, then it would be an Exponential decay.

Also b= 1+r,  where r is the rate of decay or growth.

For the given function [tex]f(x) = (0.07)^x[/tex], we can see than b= 0.07.

0.07 is less than 1.

Therefore, it would be an Exponential decay.

Now, let us find rate of decay.

1+r = 0.07.

Subtracting both sides by 1, we get

r = 0.07-1 = -0.93.

In percentage it would be 93%.

Therefore, correct option would be

D. Exponential decay of 93%





Shana uses a probability simulator to pull colored stars from a bag 60 times and to flip a coin 60 times. The results are shown in the tables below:

Color of Star

Number of Times Pulled

Pink
17

Yellow
19

Violet
24

Heads 26

Tails 34

Using Shana's simulation, what is the probability of pulling a pink star and the coin landing on tails?
fraction 578 over 3,600
fraction 646 over 3,600
fraction 34 over 60
fraction 51 over 60

Answers

17/60x34/60=578/3600
So I think it is A. 

Hope I helped you (: 

At a wedding reception, an equal number of guests were seated at 12 round tables. The 13 people in the wedding party were seated at a rectangular table. There were 121 people at the reception altogether. Which equation could you use to find the number of guests, n, seated at each round table?

Answers

12n + 13 = 121
-13 from both sides

12n = 108
÷12 from both sides

n=9

help??????

Referring to the Fig. in Question #19, write the equation in standard form of the horizontal line through the point (3,0).

Answers

You'll have to supply Question 19.

Answer:

the answer is y=0

Step-by-step explanation:

What is LCD of the fraction 1/3 and 3 1/4

Answers

LCD = 12
Thanks (:
!!!!!!!!
Answer:  The LCD (lowest common denominator) of the fractions "1/3" and "1/4" is:  "12" .
_____________________________________________________

SungHee empties her piggy bank and finds that she has 200 quaters,150 dimes,and 300 pennies.How much money does she have?Explain

Answers

9,800 coins or somethin
thats what i got.

Solve for x: |2x + 6| − 4 = 20

Answers

the answer is x= 9 or x=-15
| 2x +6 |= 16
2x+6 =16  or 2x+6 = -16
2x=10 or 2x= 22
x= 5  or x=11

21 is what percent of 42

Answers

21 is 50% of 42. 
42 x 0.5 = 21
1. We assume, that the number 42 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 42, so we can write it down as 100%=42.
4. We know, that x% equals 21 of the output value, so we can write it down as x%=21.
5. Now we have two simple equations:
1) 100%=42
2) x%=21
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=42/21
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 21 is what percent of 42

100%/x%=42/21
(100/x)*x=(42/21)*x       - we multiply both sides of the equation by x
100=2*x       - we divide both sides of the equation by (2) to get x
100/2=x
50=x
x=50

now we have:
21 is 50% of 42

Find the length of XZ
geometry help

Answers

so all the sides are equal so you'd want to set 2x = (5/2)x - 5. then solve the equation and x = 10

to solves the equation first subraxt (5/2)x from both sides and you wnd up with -0.5x = -5 then divide by -0.5 to get x = 10
hope this helped!

how do i write a direct variation given that y varies directly with x
x: 15 y: -5

Answers

When we say that y varies directly with x, we mean that whatever value x is scaled up by, y will be scaled up by, too. The simplest kind of direct variation is one where y = x for all values of x. If you multiply x by some value, y must be multiplied by that same value.

More generally, though, you'll have something of the form y = kx, where the variable k here is referred to as the constant of proportionality. Another way you can think of k is as the ratio of y to x.

In this problem, you're given a set of values for x and y, and you'll need to use those to find the constant of proportionality before you set up an equation relating x to y. Substituting our general equation y = kx for the given values, we have:

-5 = k(15)

To get k, simply divide both sides by 15 to obtain:

k = -5/15 = -1/3

So, our general equation, for any x, would be y = (-1/3)x

GCF 6x and 20xyz please help

Answers

GCF stands for "greatest common factor". This means what is the largest quantity you can divide into 6x and 20xyz without a remainder. First see what is the biggest number you can divide 6 by and also 20 without having a remainder. Next, you should see which variables 6x and 20xyz have in common. variables are the (x,y, and z). Put these two values togther and this will be your GCF.
Final answer:

The Greatest Common Factor (GCF) of 6x and 20xyz is determined by factorizing both terms and finding the common factors. Through this process, we find that 2x is the GCF.

Explanation:

The question is asking for the Greatest Common Factor (GCF) of 6x and 20xyz. The GCF is the largest number or terms that divide both numbers exactly. To find the GCF, we usually list all the factors and select the largest one that is common to both. Let's break down the terms:

Write down the factorizations of each term, i.e., 6x= 2*3*x and 20xyz = 2*2*5*x*y*z.Find the common factors. In this case, we have 2 and x in common.2*x = 2x, so 2x is the GCF.

Therefore, the greatest common factor of 6x and 20xyz is 2x.

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If 1 liter = 1.057 quarts, how many quarts are in 1 kiloliter?

Answers

1 Liter = 1.057 quarts 1 kiloliter is 1000 liter = 1057 quarts.
The answer may be 10000

Fifteen children voted their favorite color. The votes for red and blue together were double the votes for green and yellow together.How did the children vote?

Answers

5 green and yellow, ten red and blue
15, = 5 x 3 = 3 groups of five children of,  5 groups of 3 children, They voted in groups, their were no doubles.

What do the numbers listed for an element on the periodic table represent?

The smaller number is the mass, and the greater number is the atomic number.
The smaller number is the number of protons, and the greater number is the mass.
The smaller number is the number of neutrons, and the greater number is the number of electrons.
The smaller number is the number of neutrons, and protons and the greater number is the number of electrons.

Answers

Im sure you have your answer by now but would you mind posting the answer

Answer:

The smaller number is the atomic number or the number of protons and the larger number is the atomic mass.

Explained:

The number with a lower value is the number of protons and the number with a higher value is the mass.

 

The periodic table is a tabular arrangement of the chemical elements, ordered by their atomic number (number of protons), electron configurations, and recurring chemical properties.

 

The correct answer between all the choices given is the first choice or letter A. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

Monisha and Dave each sold more magazine subscriptions as part of a fundraiser Monisha rays have as much money as the rays together the race $213.75 what is the total amount of money the money she has raised

Answers

Monisha = x/2

Dave = x

x + (x/2) = 213.75

1. Solve for x.

2. Evaluate x/2 to find the total amount raised by Monisha.

Take it from here.

Is it possible to divide 15 by a mixed number an get a quotient greater than 15

Answers

If the mixed number can be anything less than 1 then sure, but I don't think 0 can be the whole number part of a mixed number, or at least I've never seen it
no you cannot because you are dividing a number greater than one.

When is A divided by B equal to an integer? Explain please.

Answers

Can't see all the options. 

However, I'll guess and suggest B.

Not sure if this helped at all :P

The amount of money left in Alma’s bank account is expressed by the linear equation y = -27x + 577, where x represents the number of weeks and y represents the amount of money left in her account. After how many weeks will Alma have $145 left in her account?

Answers

Answer:

16

Step-by-step explanation:

Answer:

B: 16 weeks

Step-by-step explanation:

If we are given the equation y = -27x + 577 and that

x = weeks

y = money left in account

Then you must replace 145 (the money) for y and solve for x (the weeks)

145 = -27x + 577

145 - 577 = -27x + 577 - 577

-432 = -27x

-432/-27 = -27x/-27

16 = x

This means that after 16 weeks Alma will have $145 left in her account

Hope this helped!

Julie has a bag of p blue marbles and q red marbles in the ratio 2:3. She adds r blue marbles. The ratio of blue marbles to red marbles is now 2:1. What is the ratio between p and r

Answers

I'm not sure how to answer the question... BUT, I know that the side that says 2 is for the blue marbles and 1 is for the red marbles, meaning that every 2 blue marbles she has equal 1 red marble. 
Sorry I didn't have the answer, hope this helps :/

If 2 and 4 each divide q without remainder which of the following must q divide without remainder

Answers

i would say that it is because the answer cannot be determined from the information given.
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