What is the decimal equivalent of 3 `5/8`?

Options

A. 3.58
B. 3.85
C. 3.65
D. 3.625

Answer

To find the decimal equivalent of \(3 \frac{5}{8}\), we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
A mixed number can be converted to an improper fraction using the formula:
\[ \text{Improper Fraction} = a \times c + b \quad \text{where } a \text{ is the whole number, } b \text{ is the numerator, and } c \text{ is the denominator.} \]
For \(3 \frac{5}{8}\):
- \(a = 3\)
- \(b = 5\)
- \(c = 8\)

So, we calculate:
\[ 3 \times 8 + 5 = 24 + 5 = 29 \]
Thus, \(3 \frac{5}{8} = \frac{29}{8}\).

### Step 2: Divide the numerator by the denominator
Now, we need to divide \(29\) by \(8\) to convert the improper fraction to a decimal.
\[ 29 \div 8 \]
- \(8\) goes into \(29\) three times (since \(8 \times 3 = 24\)).
- Subtract \(24\) from \(29\) to get a remainder of \(5\).

### Step 3: Add a decimal point and continue dividing
Since there is a remainder, we can add a decimal point and a zero to continue the division:
\[ 5.0 \div 8 \]
- Bring down a zero to make it \(50\).
- \(8\) goes into \(50\) six times (since \(8 \times 6 = 48\)).
- Subtract \(48\) from \(50\) to get a remainder of \(2\).

### Step 4: Continue the division
Now, we have \(2.0\) to divide:
\[ 20 \div 8 \]
- \(8\) goes into \(20\) two times (since \(8 \times 2 = 16\)).
- Subtract \(16\) from \(20\) to get a remainder of \(4\).

### Step 5: Continue dividing again
Now, we have \(4.0\) to divide:
\[ 40 \div 8 \]
- \(8\) goes into \(40\) five times (since \(8 \times 5 = 40\)).
- Subtract \(40\) from \(40\) to get a remainder of \(0\).

### Final Result
Putting it all together, we have:
\[ 3 \frac{5}{8} = 3.625 \]

Thus, the decimal equivalent of \(3 \frac{5}{8}\) is \(3.625\).

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