Use long division to convert 2 7/16 to a decimal
A 2.716
B 0.4375
C 2.2857
D 2.4375
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.
To convert 2 7/16 to a decimal using long division, follow these steps:
Step 1: Multiply the whole number (2) by the denominator (16), and then add the numerator (7).
2 * 16 = 32
32 + 7 = 39
Step 2: Write down the result from Step 1 (39) as the numerator and write down the denominator (16) as it is.
Numerator: 39
Denominator: 16
Step 3: Perform long division by dividing the numerator (39) by the denominator (16).
39 ÷ 16 = 2 remainder 7
Step 4: Write down the quotient (2) and the remainder (7) as a fraction.
Quotient: 2
Remainder: 7
Step 5: Write the remainder (7) as a fraction with the original denominator (16).
Remainder: 7
Denominator: 16
Step 6: Add the quotient (2) to the fraction from Step 5.
2 + 7/16 = 2 7/16
Therefore, the decimal form of 2 7/16 is not any of the given options (A, B, C, D).
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: Set up the long division.
2. r0
---------------------
16 | 39
Step 3: Divide the first digit of the dividend (3) by the divisor (16).
3 divided by 16 is 0 with a remainder of 3. Write down the quotient (0) above the line.
2.0 r0
---------------------
16 | 39
Step 4: Bring down the next digit (9) from the dividend.
Now we have 39.
2.0 r0
---------------------
16 | 39
Step 5: Divide the new dividend (39) by the divisor (16).
39 divided by 16 is 2 with a remainder of 7. Write down the quotient (2) above the line.
2.2 r0
---------------------
16 | 39
Step 6: Bring down the next digit (0) from the dividend.
Now we have 7.
2.2 r0
---------------------
16 | 39
Step 7: Divide the new dividend (7) by the divisor (16).
Since 7 is smaller than 16, we need to add a decimal point and zeros to the dividend. Divide 70 by 16.
2.2 r0
---------------------
16 | 39
-32
70
-64
We get 4 with a remainder of 6. Write down the quotient (4) above the line.
2.24 r0
---------------------
16 | 39
-32
70
-64
Step 8: Bring down the next digit (0) from the dividend.
Now we have 60.
2.24 r0
---------------------
16 | 39
-32
70
-64
64
Step 9: Divide the new dividend (64) by the divisor (16).
64 divided by 16 is 4 with no remainder. Write down the quotient (4) above the line.
2.244 r0
---------------------
16 | 39
-32
70
-64
64
Step 10: Since there is no remainder left, the division is complete.
Step 11: Combine the whole number quotient and the decimal portion to get the final decimal.
The final decimal is 2.4375.
Therefore, the answer is D) 2.4375.