Respuesta :
THE ANSWER FOR QUESTION 1. Answer:
THE ANSWER FOR QUESTION 2.Answer:
THE ANSWER FOR QUESTION 3. Step 1: 0.36 = 36⁄1000
Step 2: Simplify 36⁄1000 = 9⁄250
0.363636363636..................=411
Explanation:Le x=0.363636363636..................
Now as there are two digits repeating immediately after decimal point, we multiply above by 100 and get
100x=36.363636363636..................
Now subtracting first equation from second we get
99x=36 and hence x=3699=9×49×11=411
THE ANSWER FOR QUESTION 2.Answer:
To find out what is 0.36… as a fraction, identify the repeating sequence or pattern, known as reptend or repetend of 0.36 recurring.
The infinitely-repeated digit sequence of 0.36… can be indicated by three periods. For example, 0.3666… as a fraction (repeating 6, the last digit) = 11/30 .
Alternatively, a vinculum, that is a horizontal line, can be drawn above the repetend of the fraction of 0.36. In addition, one can sometimes see the period enclosed in parentheses ().
Here, we use the overlined notation to denote 0.36 repeating as a fraction:
0.36 = 11/30
0.36 = 4/11
These results for 0.36 repeating as a fraction are approximations and limited to three digits fractions. For different periods, higher precision and more results use the calculator below
THE ANSWER FOR QUESTION 3. Step 1: 0.36 = 36⁄1000
Step 2: Simplify 36⁄1000 = 9⁄250
Answer:
Part 1).
let, [tex]x=0.\overline{36}[/tex]
x = 0.363636... _______(1)
multiply both sides by 100, we get
100x = 36.363636... ______(2)
Subtract equation (1) from (2),
100x - x = ( 36.363636... ) - ( 0.363636... )
99x = 36
[tex]x=\frac{36}{99}[/tex]
[tex]x=\frac{12}{33}[/tex]
Therefore, [tex]0.\overline{36}[/tex] in simplest form is [tex]\frac{12}{33}[/tex].
Part 2).
let, [tex]x=0.3\overline{6}[/tex]
x = 0.3666... _______(1)
multiply both sides by 10, we get
10x = 3.6666... ______(2)
Subtract equation (1) from (2),
10x - x = ( 3.6666... ) - ( 0.3666... )
9x = 3.3
[tex]x=\frac{3.3}{9}[/tex]
[tex]x=\frac{33}{90}[/tex]
[tex]x=\frac{11}{30}[/tex]
Therefore, [tex]0.3\overline{6}[/tex] in simplest form is [tex]\frac{11}{30}[/tex].
Part 3).
let, [tex]x=0.36[/tex]
In fraction, we get
[tex]x=\frac{36}{100}[/tex]
[tex]x=\frac{9}{25}[/tex]
Therefore, [tex]0.36[/tex] in simplest form is [tex]\frac{9}{25}[/tex].