Question

Find the rational form of the recurring rational 0.2333333333

Answer 1

Answer:

7/30

Step-by-step explanation:

23-2/90=21/90=7/30

Answer 2

Answer:

   The rational form of the recurring rational 0.2333333333 is $\frac{7}{30}$.

Explanation:

• A repeating decimal also known as a recurring decimal is a number whose decimal representation becomes a periodic one, which means the same sequence of digits repeats indefinitely.
• A repeating decimal or a recurring decimal is the decimal representation of a number whose digits are periodic in nature and the infinitely repeated portion is not zero.
• Here given that the recurring rational number is 0.2333333333
• We have to find out the rational form of the recurring rational 0.2333333333
• Here in this recurring rational "zero point two" followed by an infinite number of threes. Since there is only one repeating digit "three", we shift the number one column to the left by multiplying by "ten" one time and subtract the original number from this. This will eliminate the repeating "threes" and we are left with 2.1

0.2333333333 × 10 = 2.333333333

Then subtract the original number from this;

⇒ 2.333333333 - 0.2333333333 = 2.1

• We can write it as an equation; "Ten" times the fraction, minus the fraction equals "two point one".

(10 × fraction) - fraction = 2.1

• It can be simplify to "nine" times the fraction equals "two point one".

(9 × fraction) = 2.1

• Dividing both sides of the equation by "nine", eliminates the nines on the left. Now we can see that our fraction is equal to "two point one" over "nine". But we know that a fraction's numerator and denominator must be integers. We can solve this problem by multiplying the top and bottom of the fraction by "ten" to create two integers in numerator and denominator.
• This gives us "twenty one - ninetieths". It can be reduced to "seven - thirtieths".

$\frac{(9 * fraction)}{9}$ = $\frac{2.1}{9}$

⇒ fraction = $\frac{2.1}{9}$

⇒ fraction = $\frac{2.1*10}{9*10}$ = $\frac{21}{90}$

By simplifying this number $\frac{21}{90}$, we get $\frac{7}{30}$.

• Therefore, the rational form of the recurring rational 0.2333333333 is $\frac{7}{30}$.

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