Difference of the largest and smallest of `(13)/(100),(5)/(4),(9)/(20),(21)/(25)` is

Options

A. `0.112`
B. `1.12`
C. `11.2`
D. `0.0112`

Answer

To solve the problem of finding the difference between the largest and smallest fractions among the given options, we will follow these steps:

### Step 1: Convert each fraction to decimal form
We will convert each of the fractions to their decimal equivalents for easier comparison.

1. **Convert \( \frac{13}{100} \)**:
\[ \frac{13}{100} = 0.13 \]

2. **Convert \( \frac{5}{4} \)**:
\[ \frac{5}{4} = 1.25 \]

3. **Convert \( \frac{9}{20} \)**:
\[ \frac{9}{20} = 0.45 \]

4. **Convert \( \frac{21}{25} \)**:
\[ \frac{21}{25} = 0.84 \]

### Step 2: Identify the largest and smallest values
Now that we have the decimal equivalents, we can identify the largest and smallest values among them.

- The values we have are:
- \( 0.13 \)
- \( 1.25 \)
- \( 0.45 \)
- \( 0.84 \)

- **Largest value**: \( 1.25 \) (from \( \frac{5}{4} \))
- **Smallest value**: \( 0.13 \) (from \( \frac{13}{100} \))

### Step 3: Calculate the difference
Now we will find the difference between the largest and smallest values.

\[ \text{Difference} = \text{Largest} - \text{Smallest} = 1.25 - 0.13 \]

### Step 4: Perform the subtraction
Now we perform the subtraction:

\[ 1.25 - 0.13 = 1.12 \]

### Final Answer
The difference between the largest and smallest fractions is:
\[ \boxed{1.12} \]