Which is the correct ascending order of the given numbers ?
A. `(3)/(7), 0.3, (2)/(7)`
B. `0.3, (2)/(7), (3)/(7)`
C. `(2)/(7), 0.3, (3)/(7)`
D. `(2)/(7), (3)/(7), 0.3`

Options

A. B
B. A
C. C
D. D

Answer

To find the correct ascending order of the given numbers \( \frac{3}{7}, 0.3, \frac{2}{7} \), we will follow these steps:

### Step 1: Convert all numbers to a common denominator
We will convert all the numbers to have a common denominator for easier comparison. The denominators we have are 7 and 10. The least common multiple (LCM) of 7 and 10 is 70.

### Step 2: Convert \( \frac{3}{7} \) to a denominator of 70
To convert \( \frac{3}{7} \) to a denominator of 70, we multiply both the numerator and denominator by 10:
\[ \frac{3}{7} = \frac{3 \times 10}{7 \times 10} = \frac{30}{70} \]

### Step 3: Convert \( 0.3 \) to a fraction with a denominator of 70
To convert \( 0.3 \) to a fraction, we can express it as \( \frac{3}{10} \). Now, we will convert it to a denominator of 70 by multiplying both the numerator and denominator by 7:
\[ 0.3 = \frac{3}{10} = \frac{3 \times 7}{10 \times 7} = \frac{21}{70} \]

### Step 4: Convert \( \frac{2}{7} \) to a denominator of 70
To convert \( \frac{2}{7} \) to a denominator of 70, we multiply both the numerator and denominator by 10:
\[ \frac{2}{7} = \frac{2 \times 10}{7 \times 10} = \frac{20}{70} \]

### Step 5: Compare the fractions
Now we have all the numbers with a common denominator of 70:
- \( \frac{2}{7} = \frac{20}{70} \)
- \( 0.3 = \frac{21}{70} \)
- \( \frac{3}{7} = \frac{30}{70} \)

Now we can compare:
- \( 20 < 21 < 30 \)

### Step 6: Write the numbers in ascending order
From the comparison, we can see that:
\[ \frac{2}{7} < 0.3 < \frac{3}{7} \]

Thus, the correct ascending order is:
\[ \frac{2}{7}, 0.3, \frac{3}{7} \]

### Final Answer
The correct option is **C: \( \frac{2}{7}, 0.3, \frac{3}{7} \)**.

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