Use long division to convert
6
7/15
to a decimal.
To convert 6 7/15 to a decimal using long division, we follow the steps below:
1. Set up the division problem: Write 6 7/15 as a fraction, which is 97/15. We will divide 97 by 15.
______
15 │ 97
2. Perform the first step of long division: Divide the first digit of the dividend (97) by the divisor (15). The quotient is 6.
6
15 │ 97
3. Multiply the quotient (6) by the divisor (15), and subtract the result from the dividend (97):
6 * 15 = 90
97 - 90 = 7
6
15 │ 97
- 90
---
7
4. Add a decimal point to the quotient and bring down a zero to continue the division process:
6.
15 │ 97
- 90
---
70
5. Perform the next step of long division: Divide the new dividend (70) by the divisor (15). The quotient is 4:
6.4
15 │ 97
- 90
---
70
- 60
---
10
6. Repeat the previous step, multiplying the new quotient (4) by the divisor (15), and subtracting the result from the dividend (10):
6.46
15 │ 97
- 90
---
70
- 60
---
10
- 10
----
0
7. Since the new dividend is 0, there are no more digits to bring down. Therefore, the division process is complete.
The final answer is 6 7/15 = 6.46 (rounded to two decimal places).
To convert the fraction 67/15 to a decimal using long division, follow these steps:
Step 1: Set up the division
Write the fraction in the long division format:
____
15| 67
Step 2: Divide
Divide the first digit of the dividend (67) by the divisor (15), and write the quotient (4) above the division bar. Multiply the divisor (15) by the quotient (4), and write the product (60) below the dividend.
4
15| 67
-60
Step 3: Subtract
Subtract the product (60) from the first part of the dividend (67 - 60 = 7). Write the result (7) below the line.
4
15| 67
-60
7
Step 4: Bring down
Bring down the next digit of the dividend (0) beside the result (7).
4
15| 67
-60
7
0
Step 5: Divide
Divide the new number (70) by the divisor (15), and write the quotient (4) above the line. Multiply the divisor (15) by the quotient (4), and write the product (60) below the dividend.
44
15| 670
-60
7
0
Step 6: Subtract
Subtract the product (60) from the dividend (70 - 60 = 10). Write the result (10) below the line.
44
15| 670
-60
7
0
10
Step 7: Bring down
Bring down the next digit of the dividend (0) beside the result (10).
44
15| 670
-60
7
0
10
0
Step 8: Divide
Divide the new number (100) by the divisor (15), and write the quotient (6) above the line. Multiply the divisor (15) by the quotient (6), and write the product (90) below the dividend.
446
15| 6700
-60
7
0
10
0
-90
Step 9: Subtract
Subtract the product (90) from the dividend (100 - 90 = 10). Write the result (10) below the line.
446
15| 6700
-60
7
0
10
0
-90
10
Step 10: Bring down
Since there are no digits remaining in the dividend, write a zero (0) below the line.
446
15| 6700
-60
7
0
10
0
-90
10
0
Step 11: Divide (Final Step)
Divide the new number (100) by the divisor (15), and write the quotient (6) above the line. Multiply the divisor (15) by the quotient (6), and write the product (90) below the dividend.
4466
15| 67000
-60
7
0
10
0
-90
10
0
-90
0
Step 12: The Decimal Result
The long division process ends when there is no remainder left. At this point, the decimal result of 67/15 is 4.4667.
To convert the fraction 6 7/15 to a decimal using long division, follow these steps:
Step 1: Set up the division
Write the fraction as a division problem by placing the numerator (6) inside the long division symbol and the denominator (15) on the outside.
_______
15 | 6
Step 2: Divide
Divide the first digit of the numerator (6) by the denominator (15). In this case, 6 ÷ 15 = 0.4. Write this result (0.4) above the division symbol as the first decimal place.
_______
15 | 6.
Step 3: Multiply
Now, multiply the decimal part you just obtained (0.4) by the denominator (15). In this case, 0.4 × 15 = 6.
0.4 * 15 = 6
Write this product (6) directly underneath the numerator.
_______
15 | 6.
- 6
Step 4: Subtract
Subtract the product from the numerator. In this case, 6 - 6 = 0.
_______
15 | 6.
- 6
__
0
Step 5: Bring down the next digit
If there are more digits in the numerator, bring down the next digit. In this case, there are no more digits after 0.
_______
15 | 6.
- 6
__
0
Step 6: Add trailing zeros
To convert the fraction to a decimal, add trailing zeros after the decimal point.
_______
15 | 6.0000
- 6
__
0
Step 7: Continue the process
Continue dividing by 15 and bringing down zeros until you obtain the desired level of precision.
_______
15 | 6.0000
- 6
__
00
- 00
___
000
- 000
____
0000
- 0000
____
Since the result is 0 with no other digits remaining, the decimal representation of 6 7/15 is approximately 0.4