Use long division to convert 6 7/15 to a decimal.

Answer 1

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...