Use long division to convert 2 to a decimal 7/16
To convert 2 to a decimal, we can use long division.
First, we set up the division problem by dividing 2 by 7/16:
0.
---------------
7/16) 2
We start by seeing how many times 7/16 goes into 2. Since 7/16 is less than 2, we know that it goes 0 times.
Next, we bring down the next digit from the dividend (2):
0.
---------------
7/16) 2
-
0.
---------------
7/16) 20
Now we divide 7/16 into 20. 7/16 goes into 20, 2 times. So we write a 2 above the line and multiply 7/16 by 2, and write the result below:
2
---------
7/16) 20
14
------
6
After subtracting 14 from 20, we have a remainder of 6.
Since the remainder is not zero, we can continue the long division by bringing down another digit (0) from the dividend:
0.2
---------
7/16) 20
14
------
6
0
Next, we divide 7/16 into 60. 7/16 goes into 60, 8 times. So we write an 8 above the line and multiply 7/16 by 8, and write the result below:
0.28
---------
7/16) 20
14
------
6
0
56
------
4
After subtracting 56 from 60, we have a remainder of 4.
Since the remainder is not zero, we can continue the long division by bringing down another digit (0) from the dividend:
0.28
---------
7/16) 20
14
------
6
0
56
------
4
0
Next, we divide 7/16 into 40. 7/16 goes into 40, 5 times. So we write a 5 above the line and multiply 7/16 by 5, and write the result below:
0.285
---------
7/16) 20
14
------
6
0
56
------
4
0
35
------
5
After subtracting 35 from 40, we have a remainder of 5.
Since the remainder is not zero, we can continue the long division by bringing down another digit (0) from the dividend:
0.2857
---------
7/16) 20
14
------
6
0
56
------
4
0
35
------
5
0
Next, we divide 7/16 into 50. 7/16 goes into 50, 7 times. So we write a 7 above the line and multiply 7/16 by 7, and write the result below:
0.285714
---------
7/16) 20
14
------
6
0
56
------
4
0
35
------
5
0
49
------
1
After subtracting 49 from 50, we have a remainder of 1.
Since the remainder is not zero, we can continue the long division process indefinitely to find more decimal places. However, for simplicity, we will stop here.
Therefore, 2 as a decimal is approximately 0.2857.
To convert the fraction 7/16 to a decimal using long division, follow these steps:
1. Write down the fraction 7/16.
7/16
2. Place the decimal point above the division bar directly above the dividend (7).
.-----
7/16
3. Determine how many times the divisor (16) can be divided into the dividend (7). In this case, it cannot be divided, so write a zero above the decimal point.
.0----
7/16
4. Multiply the divisor (16) by the number above the decimal point (0), and write the result below the dividend.
.0----
7/16
0
Multiply 16 by 0: 16 x 0 = 0
5. Subtract the result obtained in step 4 from the dividend, and bring down the next digit (7).
.0----
7/16
0
-0
----
7
6. Determine how many times the divisor (16) can be divided into the new dividend (7). In this case, it goes 0 times, so write another zero above the decimal point.
.00---
7/16
0
-0
----
7
7. Multiply the divisor (16) by the number above the decimal point (0), and write the result below the new dividend.
.00---
7/16
0
-0
----
7
0
Multiply 16 by 0: 16 x 0 = 0
8. Subtract the result obtained in step 7 from the new dividend, and bring down the next digit (0).
.00---
7/16
0
-0
----
7
0
- 0
----
0
9. Determine how many times the divisor (16) can be divided into the new dividend (0). Since the dividend is now 0, there is no need to continue further.
.0025
10. Write the final answer as a decimal by placing the decimal point above the division bar and adding the remainder of 0 at the end.
The fraction 7/16 as a decimal is approximately 0.4375.
To convert a fraction to a decimal using long division, follow these steps:
Step 1: Set up the long division expression by placing the dividend (7) inside the long division symbol (÷) and the divisor (16) outside the symbol:
_________
16 | 7
Step 2: Divide the first digit of the dividend (7) by the divisor (16). In this case, you cannot divide 7 by 16, so you need to add a decimal point above the division symbol and a zero next to the 7:
.0_______
16 | 7.0
Step 3: Multiply the divisor (16) by the quotient digit from the previous step (0), and subtract the result from the previous dividend. Write the remainder below the division line:
.0_______
16 | 7.0
- 0
The remainder is 7.
Step 4: Bring down the next digit from the dividend, which is 0, and place it next to the remainder:
.0_______
16 | 7.0
- 0
0
Step 5: Divide the new dividend (70) by the divisor (16) and write the quotient above the division line. In this case, 70 divided by 16 is 4 with a remainder of 6:
.04_______
16 | 7.0
- 0
0
- 64
6
Step 6: Repeat steps 3 to 5 until you have enough decimal places or you find a repeating pattern. In this case, you can see that 6 is repeating:
.04_______
16 | 7.0
- 0
0
- 64
6
- 64
0
Step 7: Write the final decimal by placing a decimal point in front of the repeating digit(s):
The decimal equivalent of 7/16 is approximately 0.4375, or simply 0.4 recurring (0.4̅).
Therefore, 2/7 can be expressed as approximately 0.4 recurring (0.4̅).