Use long division to convert 6 7/15 to a decimal.(1 point)
Responses
≈6.47
approximately equals 6.47
≈6.14285
approximately equals 6.14285
≈0.46
approximately equals 0.46
6.715
The correct answer is ≈6.47.
To convert 6 7/15 to a decimal using long division, we can follow these steps:
1. Write down 6 as the whole number part.
2. Convert the fraction 7/15 to a decimal by dividing the numerator (7) by the denominator (15).
- 7 ÷ 15 = 0.4666666...
3. If we stop at the second decimal place, the value is approximately 0.47.
4. Add the whole number part (6) and the decimal part (0.47) together.
- 6 + 0.47 = 6.47
Therefore, 6 7/15 as a decimal is approximately equal to 6.47.
To convert 6 7/15 to a decimal using long division, follow these steps:
1. Multiply the whole number (6) by the denominator of the fraction (15) and add the numerator (7) to get the total numerator: 6 * 15 + 7 = 97.
2. Write 97 as the dividend (the number you will divide) and write the divisor (15) outside the long division bracket.
3. Perform long division by dividing 97 by 15:
- Start with the first digit of the dividend (9) and divide it by the divisor (15): 9 ÷ 15 = 0 (bring down the next digit).
- Write down the quotient (0) and multiply it by the divisor: 0 * 15 = 0.
- Subtract the result from the first digit of the dividend: 9 - 0 = 9. Bring down the next digit (7).
- Divide this new dividend (97) by the divisor (15): 97 ÷ 15 ≈ 6.
- Write down the quotient (0.6) and multiply it by the divisor: 0.6 * 15 = 9.
- Subtract the result from the new dividend: 97 - 90 = 7.
4. Bring down the next digit (0), making the new dividend 70. Divide 70 by the divisor: 70 ÷ 15 = 4.
5. Write down the quotient (0.64), and multiply it by the divisor: 0.64 * 15 = 9.6. Subtract this value from 70: 70 - 96 = -26.
6. Since the remainder (-26) is negative, we can't continue dividing without introducing decimals.
7. To express the fraction part as a decimal, we divide the remainder (-26) by the denominator (15): -26 ÷ 15 = -1.73.
8. Finally, we add the whole number part (6) to the decimal part (0.64 - 1.73) to get the decimal equivalent of the mixed number 6 7/15: 6 + 0.64 - 1.73 ≈ 6.47.
So, the correct answer is ≈6.47.