Convert the 0.0068 Into vulgar fraction :

Options

A. `(7)/(1250)`
B. `(17)/(2500)`
C. `(17)/(5000)`
D. `(7)/(1750)`

Answer

To convert the decimal number 0.0068 into a vulgar fraction, follow these steps:

### Step 1: Identify the Decimal
The given number is 0.0068.

### Step 2: Convert to Fraction
To convert the decimal to a fraction, we can express it as:
\[ 0.0068 = \frac{68}{10000} \]
This is because there are four decimal places in 0.0068, which means we can write it as 68 over 10,000 (since 10,000 has four zeros).

### Step 3: Simplify the Fraction
Next, we need to simplify the fraction \(\frac{68}{10000}\). We can find the greatest common divisor (GCD) of 68 and 10,000.

- The prime factorization of 68 is \(2^2 \times 17\).
- The prime factorization of 10,000 is \(10^4 = (2 \times 5)^4 = 2^4 \times 5^4\).

The GCD of 68 and 10,000 is \(2^2 = 4\).

Now, we divide both the numerator and the denominator by their GCD:
\[ \frac{68 \div 4}{10000 \div 4} = \frac{17}{2500} \]

### Step 4: Final Answer
Thus, the vulgar fraction equivalent of 0.0068 is:
\[ \frac{17}{2500} \]

### Summary
The vulgar fraction equivalent to 0.0068 is \(\frac{17}{2500}\).

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