Which of the following has the largest value?

Options

A. `32/(0.05)`
B. `0.320/50`
C. `3.2/0.005`
D. `3.2/50`

Answer

To determine which of the given options has the largest value, we will evaluate each option step-by-step.

### Step 1: Evaluate Option 1 - \( \frac{32}{0.05} \)

To eliminate the decimal in the denominator, we can multiply both the numerator and denominator by 100:

\[ \frac{32}{0.05} = \frac{32 \times 100}{0.05 \times 100} = \frac{3200}{5} \]

Now, we divide:

\[ 3200 \div 5 = 640 \]

### Step 2: Evaluate Option 2 - \( \frac{0.320}{50} \)

To eliminate the decimal in the numerator, we can multiply both the numerator and denominator by 1000:

\[ \frac{0.320}{50} = \frac{0.320 \times 1000}{50 \times 1000} = \frac{320}{50000} \]

Now, we can simplify:

\[ 320 \div 50000 = 0.00064 \]

### Step 3: Evaluate Option 3 - \( \frac{3.2}{0.005} \)

To eliminate the decimals, we multiply both the numerator and denominator by 1000:

\[ \frac{3.2}{0.005} = \frac{3.2 \times 1000}{0.005 \times 1000} = \frac{3200}{5} \]

Now, we divide:

\[ 3200 \div 5 = 640 \]

### Step 4: Evaluate Option 4 - \( \frac{4}{3.2} \)

To eliminate the decimal in the denominator, we can multiply both the numerator and denominator by 10:

\[ \frac{4}{3.2} = \frac{4 \times 10}{3.2 \times 10} = \frac{40}{32} \]

Now, we can simplify:

\[ 40 \div 32 = 1.25 \]

### Summary of Values

- Option 1: \( 640 \)
- Option 2: \( 0.00064 \)
- Option 3: \( 640 \)
- Option 4: \( 1.25 \)

### Conclusion

The largest value among the options is \( 640 \), which occurs in both Option 1 and Option 3.

### Final Answer

Both Option 1 and Option 3 have the largest value of \( 640 \).

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