Match the following `:`
`{:(,"List-I",,"List-II"),(P,(2)/( 5),1.,0.70),(Q,(3)/(4),2.,0.25),(R, ( 7 )/( 10), 3., 0.40),(S, ( 1)/( 4), 4., 0.75):}`

Options

A. P-4,Q-3,R-2,S-1
B. P-3,Q-4,R-1,S-2
C. P-1,Q-2,R-3,S-4
D. P-3,Q-1,R-4,S-2

Answer

To solve the matching problem between fractions and their corresponding decimal values, we will go through each option step by step.

### Step 1: Match P with 2/5
1. **Convert the fraction 2/5 to a decimal:**
- To convert 2/5 to a decimal, we can multiply both the numerator and the denominator by 2 to make the denominator 10.
- \( \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \)
- Now, 4 divided by 10 gives us 0.4.

**Conclusion:** \( \frac{2}{5} = 0.4 \) (which corresponds to option 3).

### Step 2: Match Q with 3/4
2. **Convert the fraction 3/4 to a decimal:**
- To convert 3/4 to a decimal, we can multiply both the numerator and the denominator by 25 to make the denominator 100.
- \( \frac{3 \times 25}{4 \times 25} = \frac{75}{100} \)
- Now, 75 divided by 100 gives us 0.75.

**Conclusion:** \( \frac{3}{4} = 0.75 \) (which corresponds to option 4).

### Step 3: Match R with 7/10
3. **Convert the fraction 7/10 to a decimal:**
- The denominator is already 10, so we can directly convert it.
- 7 divided by 10 gives us 0.7.

**Conclusion:** \( \frac{7}{10} = 0.7 \) (which corresponds to option 1).

### Step 4: Match S with 1/4
4. **Convert the fraction 1/4 to a decimal:**
- To convert 1/4 to a decimal, we can multiply both the numerator and the denominator by 25 to make the denominator 100.
- \( \frac{1 \times 25}{4 \times 25} = \frac{25}{100} \)
- Now, 25 divided by 100 gives us 0.25.

**Conclusion:** \( \frac{1}{4} = 0.25 \) (which corresponds to option 2).

### Final Matching
- P matches with 3 (0.4)
- Q matches with 4 (0.75)
- R matches with 1 (0.7)
- S matches with 2 (0.25)

### Summary of Matches:
- P → 3
- Q → 4
- R → 1
- S → 2