Answer:
x = [tex]\frac{7}{30}[/tex]
Step-by-step explanation:
Given : 0.233333
To find : write as a fraction number.
Solution : We have given that
0.233333..
Let x = 0.233333.
We can see the number 3 is repeating 0.233333
So, the bar line is over the one digit 3
On multiplying the number both side by 10.
10x = 10 * 0.233333
10x = 2.33333
We can write the number 2.33333 in term of x
10x = 2.1 + x
On subtracting both sides by x
10x -x = 2.1
9x = 2.1
On dividing both sides by 9.
x = [tex]\frac{2.1}{9}[/tex]
Removing decimal
x = [tex]\frac{21}{90}[/tex] .
On dividing both number by 3
x = [tex]\frac{7}{30}[/tex]
Therefore, x = [tex]\frac{7}{30}[/tex]
⁷/₃₀
We will solve the problem of repeating decimals.
Definition:
A decimal number whose decimal part has digits which repeat endlessly is called a repeating decimal.
For example, [tex]\boxed{ \ \frac{4}{33} = 0.121212... \ }[/tex] is a repeating decimal. The three dots mean the digits in the decimal part repeat infinitely.
Notice that when we carry out the division [tex]\boxed{ \ 4 \div 33 \ }[/tex], the quotient never ends (or terminates) because zero never appears as a remainder. The block of two digits, 12, keeps appearing and no other digits appear. Often we use a bar (-) to show the block of digits which repeats in a decimal: [tex]\boxed{ \ \ 0. \overline{12} = 0.121212... \ \ }[/tex]
Given:
[tex]\boxed{ \ 0.2333333... = 0.2\overline{3} \ }[/tex]
Question:
Express it as a fractional form.
Problem Solving:
Let [tex]\boxed{ \ x = 0.2333333... \ }[/tex]
Both sides multiplied by 10.
Then [tex]\boxed{ \ 10x = 2.333333... \ }[/tex]
Let us subtract 10x by x. Subtract side by side.
[tex]\boxed{ \ 10x = 2.333333... \ }[/tex]
[tex] \ \ \boxed{ \ \ \ \ x = 0.2333333... \ }[/tex]
-_______________
[tex]\boxed{ \ \ \ 9x = 2.1 \ \ \ }[/tex]
Therefore, [tex]\boxed{ \ x = \frac{2.1}{9} \rightarrow x = \frac{21}{90} \rightarrow \frac{divided \ by \ 3}{divided \ by \ 3} \rightarrow \boxed{ \ x = \frac{7}{30} \ } \ }[/tex]
Keywords: 0.233333 as fraction, a repeating decimals, a decimal number, repeat endlessly, infinitely, the division, the quotient, subtract, 7/30
