Express `87//32` in decimal form.

Answer

To express \( \frac{87}{32} \) in decimal form, we can follow these steps:

### Step 1: Prime Factorization of the Denominator
First, we will factor the denominator, which is 32.

\[ 32 = 2^5 \]

### Step 2: Convert to Decimal Form
To convert \( \frac{87}{32} \) into decimal form, we need the denominator to be a power of 10. Since \( 32 \) is \( 2^5 \), we need to multiply the denominator by \( 5^5 \) to make it a power of 10.

### Step 3: Multiply Numerator and Denominator
We multiply both the numerator and the denominator by \( 5^5 \):

\[ \frac{87}{32} \times \frac{5^5}{5^5} = \frac{87 \times 5^5}{32 \times 5^5} \]

### Step 4: Calculate \( 5^5 \)
Now, we calculate \( 5^5 \):

\[ 5^5 = 3125 \]

### Step 5: Substitute Back
Now we substitute back into our fraction:

\[ \frac{87 \times 3125}{32 \times 3125} \]

### Step 6: Simplify the Denominator
The denominator becomes:

\[ 32 \times 3125 = 10^5 \]

### Step 7: Calculate the Numerator
Now we calculate the numerator:

\[ 87 \times 3125 = 271875 \]

### Step 8: Final Expression
Thus, we have:

\[ \frac{271875}{10^5} = 2.71875 \]

### Conclusion
The decimal form of \( \frac{87}{32} \) is:

\[ 2.71875 \]

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