Mathematics High School

convert the following repeating decimal to a fraction in simplest form .53

Answers

Answer 1

9514 1404 393

Answer:

  53/99

Step-by-step explanation:

When an n-digit repeat begins at the decimal point, the repeating digits can be placed over an equal number of 9s to make a fraction. Sometimes, that fraction can be reduced to lower terms.

  [tex]0.\overline{53}=\boxed{\dfrac{53}{99}}[/tex]

__

If the repeat does not start at the decimal point, the conversion can be done as follows.

For a number x with a decimal fraction that has n digits repeating, multiply by 10^n, subtract x and then divide by (10^n -1).

The fraction will be ...

  (x·10^n -x)/(10^n -1) . . . where x has n repeating digits in the decimal fraction

Here, that looks like ...

  [tex]x=0.\overline{53}\\100x=53.\overline{53}\\100x-x=53.\overline{53}-0.\overline{53}=53\\99x=53\\x=\dfrac{53}{99}[/tex]

Related Questions

For their summer jobs, Amanda and Julie are babysitting. Amanda starts with $150 in her savings account and
earns $15 per week. Julie starts with $200 in her savings account, and earns $5 per week. Use the following
equations to determine the number of weeks they will have the same amount of money?
Amanda's Equation: y = 15x + 150
Julie's Equation: y = 5x + 200


#28

Answers

I think the answer is that the same number will be the same at week 5


Picking Green! This is a game similar to the one you played in class, where you try
to pick as many green chips as possible before picking one white chip. One bag
has the same number of green and white chips, and the ratio of green to white
chips in the second bag is unknown. Laura and Carly completed an experiment,

Answers

Answer:

the first is a 50% chance

the second is not possible to know

Step-by-step explanation:

describe how we could create our own zero pair.

Answers

umm.... 0+0 ? 0x2 ? 0 x any number ?? lolz

Angle C and angle D are complementary. The measure of angle C is (2x)° and the measure of angle D is (3x)°. Determine the measure of the two angles.

Answers

Answer:

c=36 degrees

d=54 degrees

help with both please

Answers

Answer:

Step-by-step explanation:

Answer:b)true a)true

Step-by-step explanation:

This is my question, if you can solve this in under 2 minutes you are skilled!

Answers

Answer:

they both ate the same amount

Step-by-step explanation:

tito

1/4+3/8+1/2= 1 1/8

luis

5/8 + 1/2= 1 1/8

HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP

Answers

Answer:

i'd say it's "a" cause if I solve it for Zero I get x= 3, - 4 so x must bi bigger or equal 3

I just failed algebra for the third time someone help pls
Just tell me what to do

Answers

Answer:

study lol

Step-by-step explanation:

a cylinder has a base diameter of 10 inches and a height of 19 inches. what is it's volume in cubic inches, to the nearest tenths place? show all work and explain please !

Answers

Answer:

1492.26in

Step-by-step explanation:

which expression is equivalent to the given expression?​

Answers

Answer:

4ln x +ln 3-lnx

4ln x -ln x+ln3

3ln x+ln 3

ln(3x+3)is equivalent.

2. What type of association does this
graph show?
Positive
negative
none
all of the above

Answers

I might be wrong but I feel like it is none
None..................

I need help, this is so hard

Answers

Answer to these are in the picture I put

t/3 = 11 solve equation and check souloution what is t

Answers

Answer:                         t=33

Step-by-step explanation:

Answer:

t = 33

Step-by-step explanation:

t/3 = 11

t = 11 × 3

t = 33

3m-2n-9+(6m)-12n+7 plz plz plz plz plz plz plz plz plz plz plz plz pzl zplz plz plz plz plz plz plz plz plz plz plz plz plz plz plz pl plz plz plz plz plz plz plz plz plz plz plz plz plz plz help me

Answers

Answer:

Hope that answers your question

the answer is 9m−14n−2

Help me with this!! Will mark Brainliest ❤️

Answers

Answer:

2Units

GOOD LUCK FOR THE FUTURE! :)

Find X
Please help asap!!

Answers

I assume X= 100, since it look like 100 degree angle is equal to X angle
X is going to be 100 degrees as well, because they are verticals angles.

prove the indicated operations.
(3-i)(4+3i)(5-2i)

Answers

Answer:

I hope if one of these help.

Step-by-step explanation:

(4 - 3i) + (2 + i )(5 - 2i)

=16 - 2i

If you simplify your answer will be: 16−2i

1) (3+2i)-(1-6i)

2) 4i+3-6+i-1

3) 5i(3-2i)

4) (5+3i)(2-3i)

5) (2+i)(2-i)

1) (3 + 2i) - (1 - 6i)

 3 + 2i - 1 + 6i

 2 + 8i

2) 4i + 3 - 6 + i - 1

  5i - 3 - 1

  5i - 4

3) 5i ( 3 - 2i )

  15i - 10i^2

  15i - 10 ( -1 )

  15i + 10

4) ( 5 + 3i ) ( 2 - 3i )

  10 - 15i + 6i - 9i^2

  10 - 9i - 9i^2

  10 - 9i - 9 ( -1 )

  10 - 9i + 9

 - 9i + 19

5) ( 2 + i ) ( 2 - i )

   4  - 2i + 2i - i^2

   4 - i^2

   4 - (-1)

   5

1) 2 + 8i

2) -4 + 5i

3) 10 + 15i

4) 19 - 9i

5) 5

The operations with imaginary numbers are equal to those of the real numbers considering i as a variable, but with a property that allows to simplify the expression more, that is that i squared equals -1. Taking this property into account, we solve the expressions like this:

1) (3 + 2i) - (1-6i) = 3 + 2i - 1 + 6i = 2 + 8i

2) 4i + 3-6 + i-1 = 5i - 4 = -4 + 5i

3) 5i (3-2i) = 5i*3 - 5i*2i = 15i - 10i^2 = 15i - 10(-1) = 15i + 10 = 10 + 15i

4) (5 + 3i) (2-3i) = 5*2 - 5 3i + 3i*2 - 3*3i^2 = 10 - 15i + 6i - 9i^2 = 10 - 9i - 9(-1) = 10 - 9i + 9 = 19 - 9i

5) (2 + i) (2-i) = 2*2 - 2*i + 2*i - i^2 = 4 - 2i + 2i - (-1) = 4 + 1 = 5

I hope one of these help:)

Easy question!!! Solve for x.

Answers

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

yes

At Silver Gym, membership is $45 per month, and personal training sessions are $35 each.
At Fit Factor, membership is $85 per month, and personal training sessions are $25 each. In
one month, how many personal training sessions would Sarah have to buy to make the total
cost at the two gyms equal?
Sarah would have to buy
personal training sessions to make the total cost at the
two gyms equal.

Answers

4 personal training sessions.
45 + 35n = 185
85 + 25n = 185
N=4

(awarding brainliest) i’m not that smart pls help.

What is the circumference of these circles using 3.14 or 22/7. (round to the nearest hundredth if necessary)

Answers

Answer:

4) (2)(4)(3.14) = 25.12 m

5) (12)(3.14) = 37.68 ft

6) (2)(2)(3.14) = 12.56 yd

3. In a right triangle, the altitude from the right angle to the hypotenuse divides the
hypotenuse into two segments. The length of the altitude is the geometric mean of the
lengths of the two segments.
A. Theorem 9.1
B. Theorem 9.2 C. Theorem 9.3

Answers

Answer:

Step-by-step explanation:

Solve the equation and enter the value of x below.
X +
+(-8) = 2
X =

Answers

Answer:

x = 10.

Step-by-step explanation:

x + (-8) = 2.

First, isolate x by adding 8 to both sides.

x = 8 + 2.

Next, solve.

x = 10.

Finally, you can come to the conclusion that x = 10. Always plug in your answer to make sure it works.

10 - 8 = 2.

2 = 2.

Fifteen pencils are sold for $750. what is the cost for 1 pencil ?

a. 20
b.50
c.30
d.100​

Answers

Answer:

b) 50

Step-by-step explanation:

750/15 = 50

A store manager earns
$
24.00
per hour. If the manager works
8
hours one day and donates
1
10
of the day’s earnings to charity, how much of the earnings are left?


Answers

Answer:

165.6=x

Step-by-step explanation:

(24.00*8)0.90=x

184.00*0.90=x

165.6=x

2.7. 8=24.

24/8= 3

3/10= 0.3

3 -0.3 =$2.7

a jogger runs 8 miles north and then 5 miles west what is the shortest distance to the nearest tenth of a mile he must travel to return to his starting point​

Answers

C=9.4 Miles hope this helps

Can someone help me?

Answers

Answer:

cos 42 = x/20

20*cos 42 = x

x = approximately 14.9 ft

Step-by-step explanation:

hope it helped

Which of the following best represents pi for the circle below?

Answers

Answer:

Pi ~ 3.14

That is probably the best measure.

Step-by-step explanation:

what is the slope of (1,3) and (1,0)​

Answers

Answer:

-3

Step-by-step explanation:

you can tell that the awnser is negative because the coordinates of Y go down from 3 to 0.

What is the output of this function when the input is 5?

Answers

Answer:

-1

Step-by-step explanation:

look at the graph, and find where x=5

where x=5, y=-1

Answer: 1

Step-by-step explanation:

just trust me bro i’m jp i got it right

Select the table that represents a linear function. (Graph them if necessary.)
Ο Α. | xo
1 2 3
y 11 8 5 2
B. x 0
X 0 1 2 3
y 0258
C. X 0
1 2 3
y 10974
O D. X 0 1 2 3
y 8 6 6175
HELP !!!!!

Answers

Answer: D

Step-by-step explanation:

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