Which number is equal to `((0.5)/(0.05)-(0.05)/(0.5))?`

Options

A. `10.1`
B. `1.10`
C. `9.9`
D. `99.0`

Answer

To solve the expression \(\frac{0.5}{0.05} - \frac{0.05}{0.5}\), we can follow these steps:

### Step 1: Convert Decimals to Fractions
First, we convert the decimals in the expression to fractions:
- \(0.5\) can be written as \(\frac{5}{10}\) (since it has one decimal place).
- \(0.05\) can be written as \(\frac{5}{100}\) (since it has two decimal places).

So, we can rewrite the expression as:
\[ \frac{\frac{5}{10}}{\frac{5}{100}} - \frac{\frac{5}{100}}{\frac{5}{10}} \]

### Step 2: Simplify Each Fraction
Now, we simplify each fraction:
1. For \(\frac{\frac{5}{10}}{\frac{5}{100}}\):
- This is equivalent to \(\frac{5}{10} \times \frac{100}{5}\) (by multiplying by the reciprocal).
- The \(5\) in the numerator and denominator cancels out, giving us \(\frac{100}{10} = 10\).

2. For \(\frac{\frac{5}{100}}{\frac{5}{10}}\):
- This is equivalent to \(\frac{5}{100} \times \frac{10}{5}\).
- Again, the \(5\) cancels out, giving us \(\frac{10}{100} = 0.1\).

### Step 3: Subtract the Results
Now we subtract the two results:
\[ 10 - 0.1 = 9.9 \]

### Final Answer
Thus, the value of the expression \(\frac{0.5}{0.05} - \frac{0.05}{0.5}\) is \(9.9\).

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