`(0.1)/(.01) + (.01)/(.1) ` is equal to

Options

A. `101/10`
B. `1101/100`
C. `11/10`
D. `1001/100`

Answer

To solve the expression \( \frac{0.1}{0.01} + \frac{0.01}{0.1} \), we will follow these steps:

### Step 1: Rewrite the decimals as fractions
We can convert the decimals into fractions:
- \( 0.1 = \frac{1}{10} \)
- \( 0.01 = \frac{1}{100} \)

So we rewrite the expression:
\[ \frac{0.1}{0.01} + \frac{0.01}{0.1} = \frac{\frac{1}{10}}{\frac{1}{100}} + \frac{\frac{1}{100}}{\frac{1}{10}} \]

### Step 2: Simplify the first fraction
To simplify \( \frac{\frac{1}{10}}{\frac{1}{100}} \), we multiply by the reciprocal:
\[ \frac{1}{10} \times \frac{100}{1} = \frac{100}{10} = 10 \]

### Step 3: Simplify the second fraction
Now we simplify \( \frac{\frac{1}{100}}{\frac{1}{10}} \):
\[ \frac{1}{100} \times \frac{10}{1} = \frac{10}{100} = \frac{1}{10} \]

### Step 4: Combine the results
Now we can combine the results from Step 2 and Step 3:
\[ 10 + \frac{1}{10} \]

### Step 5: Convert to a common denominator
To add \( 10 \) and \( \frac{1}{10} \), we convert \( 10 \) into a fraction with a denominator of 10:
\[ 10 = \frac{100}{10} \]
So now we have:
\[ \frac{100}{10} + \frac{1}{10} = \frac{100 + 1}{10} = \frac{101}{10} \]

### Final Answer
Thus, the final answer is:
\[ \frac{101}{10} \text{ or } 10.1 \]