parthsarthi748 parthsarthi748
  • 04-03-2021
  • Mathematics
contestada

Find the value of 1.999.... in the form of p
q
where p and q are integers.

Respuesta :

LammettHash
LammettHash LammettHash
  • 04-03-2021

1.999… is exactly the number 2.

Let x = 1.999… . Then 1000x = 1999.999… . Subtract x from this to eliminate the fractional part, and you get

1000x - x = 1999.999… - 1.999…

1000x - x = 1999 - 1

999x = 1998

x = 1998/999 = 2/1 = 2

So p = 2 and q = 1.

Answer Link

Otras preguntas

what does it mean to you to be a thoughtful consumer of media
What problems existed in pre revolutionary France?
what is the solution to the equation? 16+x-11=18-5
integer problems that equal 36
A gallery had 47 paintings, 75 photographs, and some sculptures. How many more paintings did the gallery have than sculptures?
The slope of a line is positive. Describe what happens to the value of x as y increases.
Colonel George Washington led a militia force into the Ohio Valley in 1754. What was the name of the fort that Washington built and was near the site of the fir
A population of black cats has been interbreeding. However, in one litter, a sole gray kitten is born. The successive generations now have a few gray cats. Whic
Diseases carried from person to person through other hosts, such as animals or insects, are known as _____
What is letter m? M/9 -17=21