Using long division to convert 2 7/16 to a decimal
To convert 2 7/16 to a decimal using long division, we can set up the problem as follows:
First, we write 2 as a fraction with a denominator of 1:
2 = 2/1
Next, we add the fraction 7/16 to 2/1:
2/1 + 7/16
To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 1 and 16 is 16. We need to find a fraction equivalent to 2/1 that also has a denominator of 16. To do this, we multiply both the numerator and denominator of 2/1 by 16:
(2/1) * (16/16) = 32/16
So, the equation becomes:
32/16 + 7/16
Now, we can add the fractions by adding the numerators together and keeping the denominator the same:
(32 + 7)/16 = 39/16
Finally, we can convert 39/16 to a decimal by dividing the numerator by the denominator:
39 รท 16 = 2.4375
Therefore, 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 an improper fraction
2 7/16 = (2 * 16 + 7)/16 = 39/16
Step 2: Perform long division by dividing the numerator (39) by the denominator (16).
2. 4 6 8 7 5
--------------------
16 | 3 9
- 3 2
------
7 0
-6 4
------
6 0
-4 8
-----
1 2
- 0
---
1 2
Step 3: Write down the quotient and bring down the next digit (0) from the dividend.
2.46875
Step 4: Repeat step 2 and 3 until you achieve the desired level of precision or the division process repeats.
Since we reached a remainder of 0, we can stop dividing. Therefore, 2 7/16 in decimal form is approximately 2.46875.
To convert the mixed number 2 7/16 to a decimal using long division, follow these steps:
Step 1: Rewrite the mixed number as an improper fraction.
To do this, multiply the whole number (2) by the denominator (16) and add the numerator (7), then place this value over the original denominator:
2 * 16 + 7 = 39
The improper fraction is 39/16.
Step 2: Perform long division.
Place the numerator (39) inside the long division sign, and the denominator (16) on the outside.
Divide 39 by 16, and write the quotient (the result of division) above the division line.
2.4375
-----------
16) 39
Divide 16 into 39: 39 divided by 16 equals 2 with a remainder of 7. Write the quotient of 2 above the division line and the remainder of 7 next to it.
2
2.4375
-----------
16) 39
-32
----
7
Step 3: Bring down the next digit.
After writing the remainder (7), bring down the next digit from the decimal number (if any). In this case, there are no more digits to bring down.
2.4375
-----------
16) 39
-32
----
7
Step 4: Continue long division.
Divide 16 into 75 (bringing down the 5 from 7/16), and write the quotient above the division line. Repeat the process if necessary until the remainder becomes 0 or begins to repeat.
2.4375
-----------
16) 39
-32
----
7
0
----
Step 5: Determine the decimal representation.
The final quotient, after the remainder becomes 0, is 2.4375, which represents the decimal equivalent of the mixed number 2 7/16.
Therefore, the decimal equivalent of 2 7/16 is 2.4375.