`(0.9894)/(0.97) - (1)/(50) = `

Options

A. `1.2`
B. `1`
C. `1.02`
D. `0.98`

Answer

To solve the expression \((0.9894)/(0.97) - (1)/(50)\), we can follow these steps:

### Step 1: Simplify the first term
We start with the division of two decimals:
\[ \frac{0.9894}{0.97} \]
To simplify this, we can eliminate the decimals by multiplying both the numerator and denominator by 100:
\[ \frac{0.9894 \times 100}{0.97 \times 100} = \frac{98.94}{97} \]

### Step 2: Perform the division
Now, we divide \(98.94\) by \(97\):
\[ 98.94 \div 97 \approx 1.0204 \]

### Step 3: Simplify the second term
Next, we simplify the second term:
\[ \frac{1}{50} \]
This remains as is.

### Step 4: Find a common denominator
To subtract the two fractions, we need a common denominator. The common denominator for \(50\) and \(100\) is \(100\):
\[ 1.0204 - \frac{1}{50} = 1.0204 - \frac{2}{100} \]

### Step 5: Rewrite the first term with a common denominator
Now we can rewrite \(1.0204\) as:
\[ \frac{1020.4}{100} \]

### Step 6: Perform the subtraction
Now we perform the subtraction:
\[ \frac{1020.4}{100} - \frac{2}{100} = \frac{1020.4 - 2}{100} = \frac{1018.4}{100} \]

### Step 7: Convert back to decimal
Now we convert the fraction back to a decimal:
\[ \frac{1018.4}{100} = 10.184 \]

### Final Answer
Thus, the final result of the expression \((0.9894)/(0.97) - (1)/(50)\) is:
\[ 10.184 \]

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