Find the fraction with denominator 120 whose decimal value is 0.65.

Options

A. `(62)/(120)`
B. `(78)/(120)`
C. `(35)/(120)`
D. `(90)/(120)`

Answer

To find the fraction with a denominator of 120 whose decimal value is 0.65, we can follow these steps:

### Step 1: Set up the equation
We need to express the fraction in the form of \( \frac{X}{120} \) where \( X \) is the numerator we need to find. Since we know that the decimal value is 0.65, we can write the equation as:

\[ \frac{X}{120} = 0.65 \]

### Step 2: Solve for X
To find \( X \), we can multiply both sides of the equation by 120:

\[ X = 0.65 \times 120 \]

### Step 3: Calculate the value of X
Now, we perform the multiplication:

\[ X = 0.65 \times 120 = 78 \]

### Step 4: Write the fraction
Now that we have found \( X \), we can write the fraction:

\[ \frac{X}{120} = \frac{78}{120} \]

### Step 5: Simplify the fraction (if necessary)
The fraction \( \frac{78}{120} \) can be simplified. To do this, we can find the greatest common divisor (GCD) of 78 and 120, which is 6.

Now, we divide both the numerator and the denominator by 6:

\[ \frac{78 \div 6}{120 \div 6} = \frac{13}{20} \]

### Final Answer
The fraction with a denominator of 120 whose decimal value is 0.65 is:

\[ \frac{78}{120} \]