Use long division to convert 2 7/16 to a decimal.
To convert 2 7/16 to a decimal using long division, we need to divide the fraction 7/16 by the whole number 2.
First, we convert the mixed number to an improper fraction:
2 7/16 = (2 × 16 + 7) / 16 = 39/16
Now, we will perform the long division:
2.4375
_______________
16 | 39.0000
- 32
_____
70
- 64
_____
60
- 48
_____
120
- 112
_____
80
- 80
_____
0
The remainder becomes 0, indicating that the division is complete. Therefore, 2 7/16 as a decimal is 2.4375.
To convert a mixed number like 2 7/16 to a decimal using long division, follow these steps:
Step 1: Rewrite the mixed number as an improper fraction.
To convert 2 7/16 to an improper fraction, multiply the whole number (2) by the denominator (16) and add the numerator (7). Then, put the result over the original denominator (16).
2 × 16 = 32
32 + 7 = 39
So, 2 7/16 as an improper fraction is: 39/16.
Step 2: Set up the long division.
Divide 39 by 16 using long division, like this:
2.4375
__________________
16 | 39
Step 3: Divide.
Divide the first digit of the dividend (39) by the divisor (16) and write the quotient above the line. Then, multiply the divisor (16) by the quotient (2) and write the result below the line, aligning the decimal points. Finally, subtract the result from the dividend and bring down the next digit (0).
2.4375
__________________
16 | 39
- 32
-----
7
Step 4: Bring down the next digit.
Since there are no more digits in the dividend, we bring down a zero and continue the division.
2.4375
__________________
16 | 39
- 32
-----
70
Step 5: Divide again.
Divide the new dividend (70) by the divisor (16) and write the quotient (4) above the line. Multiply the divisor (16) by the quotient (4) and write the result again below the line. Finally, subtract and bring down the next digit (0).
2.4375
__________________
16 | 39
- 32
-----
70
- 64
-----
6
Step 6: Divide once more.
Divide the new dividend (6) by the divisor (16) and write the quotient (0) above the line. Multiply the divisor (16) by the quotient (0) and write the result below the line.
2.4375
__________________
16 | 39
- 32
-----
70
- 64
-----
6
- 0
-----
6
Step 7: Add zeros.
Since the division is complete and there is no remainder, add zeros to the right of the decimal point in the quotient until you have the desired level of precision. In this case, the desired precision is five decimal places.
2.4375
So, 2 7/16 is equal to approximately 2.4375 as a decimal.