Repeating Decimal Addition Explained
This solution explains how to find the sum of two repeating decimals, $0.\overline{23}$ and $0.\overline{22}$.
Convert Repeating Decimals to Fractions
Repeating decimals can be accurately represented as fractions. A repeating decimal of the form $0.\overline{ab}$ is equal to the fraction $\frac{ab}{99}$.
- Convert $0.\overline{23}$: $0.\overline{23} = \frac{23}{99}$
- Convert $0.\overline{22}$: $0.\overline{22} = \frac{22}{99}$
Add the Fractions
Now, add the fractional representations:
$ \frac{23}{99} + \frac{22}{99} = \frac{23 + 22}{99} = \frac{45}{99} $Convert Sum Back to Repeating Decimal
Convert the resulting fraction $\frac{45}{99}$ back into a repeating decimal. Since the denominator is 99, the numerator represents the repeating part.
$ \frac{45}{99} = 0.454545... = 0.\overline{45} $Therefore, the value of $0.\overline{23} + 0.\overline{22}$ is $0.\overline{45}$.
Similar Questions
- Solve the following.
$3.142 + 3.61 - 2.12 + 4 - 7.6 =$ ? What will the value of the following be (correct to three decimal points)?
$160.342 - 32.124$
Arrange the following numbers in their increasing order.
(1) $-0.96$
(2) $0.83$
(3) $0.24$
(4) $-0.64$
(5) $0.58$
- Which of the following has terminal decimal representation?
- If the value of $\frac{1}{36.18}$ is $0.0276$, then what is the value of $\frac{1}{0.0003618}$?
Simplify the given expression.
$9 \times 0.9 \times 0.09 \times 0.009 \times \frac{1}{0.3} \times \frac{1}{0.03} \times \frac{1}{0.003}$- When 0.434343..... is converted into a fraction, then the result will be:
- $0.5\overline{32}$ is equivalent to the fraction:
- How will you write 2.84 hours in hours, minutes and seconds?
- Select the option that expresses $5.\overline{6}$ as a fraction.
Important Questions from Decimals
What is the result when 0.129129129… is converted to a fraction?
Which of the following statement(s) is/are correct?
I. (3/11) > 0.3
II. (7/8) > 0.86
The value of \(1.\overline{3}+0.\overline{69}-0.5\overline{23}\) is equal to:
The value of \(0.\bar 4 + 0.5 \bar 9 - 0.4 \overline{23}\) is equal to:
Find the sum of \(\frac{0.01}{0.1}+\frac{0.1}{0.01}\)
