To convert 2 7/16 to a decimal using long division, follow these steps:
Step 1: Rewrite the mixed number as an improper fraction.
2 7/16 can be written as (2 * 16 + 7) / 16 = 39/16
Step 2: Perform long division.
Start by dividing 39 by 16: 39 ÷ 16 = 2
Multiply the quotient (2) by the divisor (16): 2 * 16 = 32
Subtract this result (32) from 39: 39 - 32 = 7
Bring down the next digit (0): 70
Divide 70 by 16: 70 ÷ 16 = 4
Multiply the new quotient (4) by the divisor (16): 4 * 16 = 64
Subtract this result (64) from 70: 70 - 64 = 6
Bring down the next digit (0): 60
Divide 60 by 16: 60 ÷ 16 = 3
Multiply the new quotient (3) by the divisor (16): 3 * 16 = 48
Subtract this result (48) from 60: 60 - 48 = 12
Bring down the next digit (0): 120
Divide 120 by 16: 120 ÷ 16 = 7
Multiply the new quotient (7) by the divisor (16): 7 * 16 = 112
Subtract this result (112) from 120: 120 - 112 = 8
Bring down the next digit (0): 80
Divide 80 by 16: 80 ÷ 16 = 5
Multiply the new quotient (5) by the divisor (16): 5 * 16 = 80
Subtract this result (80) from 80: 80 - 80 = 0
Step 3: Write the final quotient as a decimal.
The final quotient is 2.4375.
Therefore, the answer is D) 2.4375.