A Fahrenheit thermometer registers `100^(@)F` while a faulty Celsius thermometer registers `44^(@)C`. Find the error in the later

Options

A. `0.37^(@)`
B. `0.87^(@)`
C. `0.67^(@)`
D. `0.48^(@)`

Explanation

To find the error in the faulty Celsius thermometer that registers \(44^\circ C\) while the Fahrenheit thermometer registers \(100^\circ F\), we will follow these steps:

### Step 1: Convert Fahrenheit to Celsius
We will use the formula to convert the temperature from Fahrenheit to Celsius:

\[ T_C = \frac{5}{9} (T_F - 32) \]

where \(T_C\) is the temperature in Celsius and \(T_F\) is the temperature in Fahrenheit. Given \(T_F = 100^\circ F\), we can substitute this value into the formula.

### Step 2: Substitute the Fahrenheit value
Substituting \(T_F = 100\) into the formula:

\[ T_C = \frac{5}{9} (100 - 32) \]

### Step 3: Calculate the difference
Now, calculate \(100 - 32\):

\[ 100 - 32 = 68 \]

### Step 4: Multiply by \(\frac{5}{9}\)
Now we will multiply \(68\) by \(\frac{5}{9}\):

\[ T_C = \frac{5}{9} \times 68 \]

### Step 5: Perform the multiplication
Calculating \(\frac{5 \times 68}{9}\):

\[ T_C = \frac{340}{9} \approx 37.78^\circ C \]

### Step 6: Determine the error
Now, we need to find the error in the faulty Celsius thermometer. The faulty thermometer reads \(44^\circ C\), while the correct value we calculated is approximately \(37.78^\circ C\). To find the error:

\[ \text{Error} = \text{Faulty Reading} - \text{Correct Reading} \]

Substituting the values:

\[ \text{Error} = 44 - 37.78 \]

### Step 7: Calculate the error
Now, perform the subtraction:

\[ \text{Error} = 6.22^\circ C \]

### Final Result
The error in the faulty Celsius thermometer is \(6.22^\circ C\).

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