# Fraction

Fraction
$\dfrac{0,\overline{ 40 }}{0,40 }$
write as fraction a/b, a, b is integers numerator/denominator.

Result

a =  100
b =  99

#### Solution:

$x = \dfrac{0,\overline{ 40 }}{0,40 } = \dfrac{1 }{0,40} \dfrac{ a_1}{1-q} = \dfrac{1 }{0,40} \dfrac{0,40}{1-\dfrac{1}{100}} \ \\ x = \dfrac{1}{1-\dfrac{1}{100}} = \dfrac{100}{99} \ \\$
$b=99$

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Stella
i like this

Bob
good

#### Following knowledge from mathematics are needed to solve this word math problem:

Need help calculate sum, simplify or multiply fractions? Try our fraction calculator.

## Next similar math problems:

1. Decimal to fraction
Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.
2. Series and sequences
Find a fraction equivalent to the recurring decimal? 0.435643564356
3. Sum of series
Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+....
4. Infinite decimal
Imagine the infinite decimal number 0.99999999 .. ... ... ... That is a decimal and her endless serie of nines. Determine how much this number is less than the number 1. Thank you in advance.
5. Infinite sum of areas
Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tri
6. Infinity
In a square with side 18 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares.
7. Recursion squares
In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 22 cm. Calculate: a) the sum of perimeters of all
8. To the cinema
Jane at 8 am got message that all 1093 school pupils will go to the cinema. Within 20 min she said it to the three friends. Each of them again for 20 minutes said to the other three. In this way the message spread further. At what time all the children in.
9. Miraculous tree
Miraculous tree grows so fast that the first day increases its height by half the total height of the second day by the third, the third day by a quarter, etc. How many times will increase its height after 6 days?
10. Hot air balloon
Hot air balloon ascends 25 meters up for a minute after launch. Every minute ascends 75 percent of the height which climbed in the previous minute. a) how many meters ascends six minutes after takeoff? b) what is the overall height 10 minutes after launch
11. Saving per cents
The first day I save 1 cent and every next day cent more. How many I saved per year (365 days)?
12. Population growth
How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years?
13. Ten dices
When you hit ten dices at the same time you get average 35. How much do you hit if every time you get six, you're throwing the dice again?
14. An animal shelter
An animal shelter spends $5.50 per day to care for each bird and$8.50 per day to care for each cat. Nicole noticed that the shelter spent \$283.00 caring for birds and cats on Wednesday. Nicole found a record showing that there were a total of 40 birds and
15. Land boundary
The land has the shape of a right triangle. The hypotenuse has a length of 30m. The circumference of the land is 72 meters. What is the length of the remaining sides of the land boundary?
16. Circular railway
The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
17. Parallels and one secant
There are two different parallel lines a, b and a line c that intersect the two parallel lines. Draw a circle that touches all lines at the same time.