Use long division to convert 2 7/16 to a decimal. (1 point)
To convert 2 7/16 to a decimal using long division, we need to divide the numerator (7) by the denominator (16).
First, we write 2 as a fraction: 2 = 2/1.
Next, we multiply the whole number (2) by the denominator (16): 2 x 16 = 32.
We add the numerator (7) to the result (32): 32 + 7 = 39.
The resulting fraction is 39/16.
Now, we perform long division:
Divide 39 by 16:
2 remainder 7
_____________
16 | 39
32
_______
7
So, 2 7/16 as a decimal is 2.4375.
To convert 2 7/16 to a decimal using long division, follow these steps:
Step 1: Write the mixed number as a fraction.
2 7/16 can be written as (2 * 16 + 7) / 16.
Step 2: Convert the mixed number to an improper fraction.
(2 * 16 + 7) / 16 = (32 + 7) / 16 = 39/16.
Step 3: Perform long division.
Divide the numerator (39) by the denominator (16).
2.4375
__________
16 ) 39.0000
Step 4: Begin the long division by dividing the first digit (3) of the numerator (39) by the denominator (16). Place the result (2) above the division bar, and multiply the divisor (16) by the result (2) and subtract it from the numerator (39).
2.4375
__________
16 ) 39.0000
- 32
________
7
Step 5: Bring down the next digit (0) from the numerator (7) and place it after the result (2) above the division bar, creating the dividend 70.
2.4375
__________
16 ) 39.0000
- 32
________
7
-0
Step 6: Divide the new dividend (70) by the denominator (16). Place the result (4) above the division bar. Multiply the divisor (16) by the result (4) and subtract it from the dividend (70).
2.4375
__________
16 ) 39.0000
- 32
________
7
- 0
_______
70
- 64
________
6
Step 7: Repeat step 5 and step 6 until there are no more digits to bring down.
Continuing with the division:
2.4375
__________
16 ) 39.0000
- 32
________
7
- 0
_______
70
- 64
________
6
- 0
________
60
- 48
________
12
- 0
________
120
- 112
_________
8
Step 8: The remainder is 8. Since there are no more digits in the dividend, the division is complete.
Step 9: Write the result with the decimal point.
The final result is 2.4375 when 2 7/16 is converted to a decimal using long division.