Use long division to convert 6 7/15 to a decimal.
A. 6.14285
B. 6.715
C. 0.46
D. 6.47
To convert 6 7/15 to a decimal using long division, follow these steps:
1. Write the mixed number as an improper fraction: 6 7/15 = (6 x 15 + 7)/15 = 97/15
2. Perform the long division: Divide 97 by 15.
6. 13
-----------------------
15) 97
90
-----
7
0
---
3. Continue the division until you either reach a recurring decimal or the desired level of precision. In this case, the decimal terminates, so we don't need to continue.
4. The final answer is 6.466667, but we are asked for the answer to the nearest hundredth.
Therefore, the answer is D. 6.47
To convert 6 7/15 to a decimal using long division, follow these steps:
Step 1: Write the mixed number as an improper fraction.
6 7/15 = (6 * 15 + 7)/15 = 97/15
Step 2: Perform long division by dividing the numerator (97) by the denominator (15).
6.467
----------
15 | 97
Step 3: Begin dividing 97 by 15. The quotient so far is 6 (indicated above the line).
6.467
----------
15 | 97
90
-----
7
Step 4: Bring down the next digit (7), and add a decimal point to the quotient above the line to make it accurate.
6.467
----------
15 | 97
90
-----
73
Step 5: Divide 73 by 15.
6.467
----------
15 | 97
90
-----
73
60
-----
13
Step 6: Bring down the next digit (0).
6.467
----------
15 | 97
90
-----
73
60
-----
130
Step 7: Divide 130 by 15.
6.467
----------
15 | 97
90
-----
73
60
-----
130
120
-----
10
Step 8: At this point, we notice that we have a repeating decimal pattern, indicated by the 10 above. Since there are no further digits to bring down, we can stop the division.
Step 9: Round the final quotient to an appropriate number of decimal places based on the original question. In this case, we round it to three decimal places.
The final answer is 6.467, which corresponds to option D.
To convert a mixed fraction (6 7/15) to a decimal, you can use long division by following these steps:
1. Start by writing the mixed fraction (6 7/15) as an improper fraction. To do this, multiply the whole number (6) by the denominator of the fraction (15), and add the numerator (7):
6 * 15 + 7 = 97
So, the improper fraction equivalent of 6 7/15 is 97/15.
2. Set up the long division by writing the numerator (97) inside the division bracket, and the denominator (15) outside the bracket:
97
------
15|
3. Begin by dividing the first digit of the numerator (9) by the denominator (15). The quotient obtained is the first decimal digit of the answer:
9 ÷ 15 = 0.6
4. Write down the decimal digit obtained (0.6) above the division line, and subtract the product of the divisor (15) and the previous quotient (0.6) from the last digit of the numerator (7):
7 - (15 × 0.6) = 7 - 9 = -2
5. Bring down the next digit of the numerator (2) to the right of the remainder (-2):
97
------
15| 0.6
6. Divide the new numerator (-2) by the denominator (15):
-2 ÷ 15 = -0.1333...
7. Write down the resulting decimal digit (-0.1333...) above the division line, and subtract the product of the divisor (15) and the previous quotient (-0.1333...) from the next digit of the numerator (2):
2 - (15 × -0.1333...) = 2 + 1.99999... ≈ 3
8. Again, bring down the next digit of the numerator (0) to the right of the remainder (3):
97
------
15| 0.64
9. Divide the new numerator (3) by the denominator (15):
3 ÷ 15 = 0.2
10. Write down the resulting decimal digit (0.2) above the division line, and subtract the product of the divisor (15) and the previous quotient (0.2) from the last digit of the numerator (0):
0 - (15 × 0.2) = 0 - 3 = -3
11. At this point, since there is no more digit to bring down, the long division process is finished. The quotient obtained is 0.64, which is equivalent to the decimal representation of the mixed fraction 6 7/15.
So, the correct answer is D. 6.47.