Use long division to convert 6 7/15 to a decimal.
To convert 6 7/15 to a decimal using long division, you can follow these steps:
1. Write the whole number part (6) as the dividend and the fraction part (7/15) as the divisor.
2. Place a decimal point at the end of the dividend.
3. Multiply the divisor (7/15) by an appropriate multiple of 10, so that it becomes a whole number. In this case, multiplying by 10 is sufficient, resulting in 70/15.
4. Perform the long division by dividing 70 by 15.
- The quotient of 70 divided by 15 is 4.
- Multiply the quotient by the original divisor to get 4 * (7/15) = 28/15.
- Subtract 28/15 from 70/15 to get a remainder of 42/15.
5. Bring down the next digit from the decimal expansion of the dividend. Since there are no more digits in the original dividend, bring down a zero.
6. Divide the new dividend 420 by 15, repeating the long division process.
- The quotient of 420 divided by 15 is 28.
- Multiply the quotient by the original divisor to get 28 * (7/15) = 196/15.
- Subtract 196/15 from 420/15 to get a remainder of 224/15.
7. Continue the long division process until you either get a remainder of zero or a repeated pattern.
- The decimal expansion of 6 7/15 is 6.466666666...
- This decimal represents a recurring decimal pattern, with 6.4 being the non-repeating part and 6 recurring after the decimal point.
Therefore, 6 7/15 as a decimal is approximately 6.466666666...
To convert a mixed number to a decimal using long division, follow these steps:
Step 1: Rewrite the mixed number as an improper fraction.
To convert 6 7/15 to an improper fraction, multiply the whole number (6) by the denominator (15) and then add the numerator (7). In this case, it would be:
6 * 15 + 7 = 97
So, 6 7/15 can be written as 97/15.
Step 2: Perform long division.
To convert the fraction 97/15 to a decimal, divide the numerator (97) by the denominator (15) using long division. Here's how you can do it:
6.4
__________
15 | 97
In this case, you start by dividing 97 by 15. The quotient (whole number in the division) is 6, which means the decimal part is 0.4.
Therefore, 6 7/15 as a decimal is 6.4.
To convert the mixed number 6 7/15 to a decimal using long division, follow these steps:
1. Write down the mixed number as a whole number plus a fraction. In this case, 6 7/15 can be written as 6 + (7/15).
2. Set up the long division problem by writing the whole number part (6) as the divisor outside the division bar and the fraction part (7/15) as the dividend inside the division bar.
---------------
6 | 7/15
3. Convert the fraction part (7/15) into a decimal. To do this, divide the numerator (7) by the denominator (15):
0.4
------
6 | 7 /15
4. Perform the long division by dividing 6 into 7/15. Start by dividing 6 into the first digit of the dividend (7).
6 goes into 7 (0 times) = 0
Multiply 0 by 6 and subtract from 7/15:
7/15 - 0 = 7/15
5. Bring down the next digit from the dividend (0 in this case).
0.4
------
6 | 7 /15
0
6. Divide 6 into the new dividend (70/15).
6 goes into 70 (11 times) = 11
Multiply 11 by 6 and subtract from 70/15:
70/15 - 66/15 = 4/15
7. Bring down the next digit from the dividend (0 in this case).
0.46
-------
6 | 7 /15
11
-------
4 /15
8. Divide 6 into the new dividend (40/15).
6 goes into 40 (6 times) = 6
Multiply 6 by 6 and subtract from 40/15:
40/15 - 36/15 = 4/15
9. Bring down the next digit from the dividend (0 in this case).
0.466
--------
6 | 7 /15
11
-------
4 /15
4
--------
0
10. Continue the process until the remainder becomes zero.
Since the remainder is now zero, the long division is complete.
11. The result of the long division is 0.466. Therefore, the mixed number 6 7/15 is equal to 6.466 when expressed as a decimal.