What percent of `3/7` is `1/105`?

Options

A. `10%`
B. `2.22%`
C. `45%`
D. `450%`

Answer

To solve the question "What percent of `3/7` is `1/105`?", we can follow these steps:

### Step 1: Set up the equation
We want to find out what percent (let's denote it as `x%`) of `3/7` is equal to `1/105`. We can express this mathematically as:

\[ \frac{x}{100} \times \frac{3}{7} = \frac{1}{105} \]

### Step 2: Rearrange the equation
To isolate `x`, we can multiply both sides of the equation by `100` and divide by `3/7`:

\[ x = \frac{1}{105} \times \frac{100 \times 7}{3} \]

### Step 3: Simplify the right side
Now, we can simplify the right side step by step:

1. Calculate \(100 \times 7 = 700\).
2. Now, we have:

\[ x = \frac{700}{3 \times 105} \]

3. Calculate \(3 \times 105 = 315\):

\[ x = \frac{700}{315} \]

### Step 4: Simplify the fraction
Next, we simplify \(\frac{700}{315}\):

1. Find the greatest common divisor (GCD) of 700 and 315. The GCD is 35.
2. Divide both the numerator and the denominator by 35:

\[ x = \frac{700 \div 35}{315 \div 35} = \frac{20}{9} \]

### Step 5: Convert to percentage
To convert \(\frac{20}{9}\) into a percentage, we multiply by 100:

\[ x = \frac{20}{9} \times 100 \approx 222.22 \]

### Step 6: Final answer
Thus, we can conclude that:

\[ x \approx 2.22\% \]

So, the answer is approximately **2.2%**.

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