Let's call the repeating decimal $a$. We can write $a$ as the sum of the original decimal, $3.8$, and the repeating part, $0.\overline{3}$:
\[a = 3.8 + 0.\overline{3}\]
To convert the repeating decimal to a fraction, we'll use the fact that $\overline{3} = \frac{3}{9}$.
So, \[a = 3.8 + 0.\overline{3} = 3.8 + \frac{3}{9}\]
Next, we'll convert the mixed number $3.8$ to an improper fraction. Multiplying the whole number, $3$, by the denominator of the fraction, $9$, and adding the numerator, $8$, we get $3\cdot 9 + 8 = 35$. So, $3.8$ is equivalent to $\frac{35}{9}$.
Substituting $\frac{35}{9}$ into the equation, we have:
\[a = \frac{35}{9} + \frac{3}{9}\]
Now we can add the fractions by adding their numerators and keeping the denominator the same:
\[a = \frac{35 + 3}{9} = \frac{38}{9}\]
Therefore, $\frac{3.8\overline{3}}{1} = \boxed{\frac{38}{9}}$.
Rewrite as a simplified fraction.
\[\large{3.8\overline{3} = ?}\]
5 answers
wrong
I apologize for the mistake. Let's try again.
To convert the repeating decimal $3.8\overline{3}$ to a fraction, we'll multiply both sides of the equation by a power of 10 to move the decimal point to the right of the repeating part. Let's multiply by 100 to get rid of the repeating part:
\[100 \cdot \left(\frac{3.8\overline{3}}{1}\right) = 100 \cdot \left(\frac{3}{1}\right) + 100 \cdot \left(\frac{0.\overline{3}}{1}\right)\]
Simplifying the left side gives:
\[383.\overline{3} = 300 + 0.\overline{3}\]
We'll call $383.\overline{3}$ as $a$ and $0.\overline{3}$ as $b$. Then we have:
\[a = 300 + b\]
To convert $b$ to a fraction, let's multiply by 10 to move the repeating part to the left of the decimal point:
\[10b = 3.\overline{3}\]
Subtracting $b$ from $10b$ eliminates the repeating part:
\[10b - b = 3.\overline{3} - 0.\overline{3}\]
Simplifying gives:
\[9b = 3\]
Dividing both sides by 9, we find that $b = \frac{3}{9} = \frac{1}{3}$.
Now we can substitute $b = \frac{1}{3}$ back into the equation $a = 300 + b$:
\[a = 300 + \frac{1}{3}\]
To add the whole number and fraction, we'll convert 300 to a fraction with the same denominator as $\frac{1}{3}$:
\[a = \frac{300}{1} + \frac{1}{3} = \frac{900}{3} + \frac{1}{3} = \frac{901}{3}\]
So, $\frac{3.8\overline{3}}{1} = \boxed{\frac{901}{3}}$.
To convert the repeating decimal $3.8\overline{3}$ to a fraction, we'll multiply both sides of the equation by a power of 10 to move the decimal point to the right of the repeating part. Let's multiply by 100 to get rid of the repeating part:
\[100 \cdot \left(\frac{3.8\overline{3}}{1}\right) = 100 \cdot \left(\frac{3}{1}\right) + 100 \cdot \left(\frac{0.\overline{3}}{1}\right)\]
Simplifying the left side gives:
\[383.\overline{3} = 300 + 0.\overline{3}\]
We'll call $383.\overline{3}$ as $a$ and $0.\overline{3}$ as $b$. Then we have:
\[a = 300 + b\]
To convert $b$ to a fraction, let's multiply by 10 to move the repeating part to the left of the decimal point:
\[10b = 3.\overline{3}\]
Subtracting $b$ from $10b$ eliminates the repeating part:
\[10b - b = 3.\overline{3} - 0.\overline{3}\]
Simplifying gives:
\[9b = 3\]
Dividing both sides by 9, we find that $b = \frac{3}{9} = \frac{1}{3}$.
Now we can substitute $b = \frac{1}{3}$ back into the equation $a = 300 + b$:
\[a = 300 + \frac{1}{3}\]
To add the whole number and fraction, we'll convert 300 to a fraction with the same denominator as $\frac{1}{3}$:
\[a = \frac{300}{1} + \frac{1}{3} = \frac{900}{3} + \frac{1}{3} = \frac{901}{3}\]
So, $\frac{3.8\overline{3}}{1} = \boxed{\frac{901}{3}}$.
WRONG!!!!!!
I apologize for the mistake.
Let's call the repeating decimal $a$. We can write $a$ as the sum of the original decimal, $3.8$, and the repeating part, $0.\overline{3}$:
\[a = 3.8 + 0.\overline{3}\]
To convert the repeating decimal to a fraction, we'll use the fact that $\overline{3} = \frac{3}{9} = \frac{1}{3}$.
So, \[a = 3.8 + 0.\overline{3} = 3.8 + \frac{1}{3}\]
Next, we'll convert the mixed number $3.8$ to an improper fraction. Multiplying the whole number, $3$, by the denominator of the fraction, $3$, and adding the numerator, $8$, we get $3\cdot 3 + 8 = 17$. So, $3.8$ is equivalent to $\frac{17}{3}$.
Substituting $\frac{17}{3}$ into the equation, we have:
\[a = \frac{17}{3} + \frac{1}{3}\]
Now we can add the fractions by adding their numerators and keeping the denominator the same:
\[a = \frac{17+1}{3} = \frac{18}{3}\]
The fraction $\frac{18}{3}$ can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:
\[a = \frac{18}{3} = \frac{6\cdot3}{3\cdot1} = \frac{6}{1} = \boxed{6}\]
Therefore, $\frac{3.8\overline{3}}{1} = \boxed{6}$.
Let's call the repeating decimal $a$. We can write $a$ as the sum of the original decimal, $3.8$, and the repeating part, $0.\overline{3}$:
\[a = 3.8 + 0.\overline{3}\]
To convert the repeating decimal to a fraction, we'll use the fact that $\overline{3} = \frac{3}{9} = \frac{1}{3}$.
So, \[a = 3.8 + 0.\overline{3} = 3.8 + \frac{1}{3}\]
Next, we'll convert the mixed number $3.8$ to an improper fraction. Multiplying the whole number, $3$, by the denominator of the fraction, $3$, and adding the numerator, $8$, we get $3\cdot 3 + 8 = 17$. So, $3.8$ is equivalent to $\frac{17}{3}$.
Substituting $\frac{17}{3}$ into the equation, we have:
\[a = \frac{17}{3} + \frac{1}{3}\]
Now we can add the fractions by adding their numerators and keeping the denominator the same:
\[a = \frac{17+1}{3} = \frac{18}{3}\]
The fraction $\frac{18}{3}$ can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:
\[a = \frac{18}{3} = \frac{6\cdot3}{3\cdot1} = \frac{6}{1} = \boxed{6}\]
Therefore, $\frac{3.8\overline{3}}{1} = \boxed{6}$.
1 answer