Use long division to convert 6 7/15

to a decimal.(1 point)
Responses

≈0.46
approximately equals 0.46

≈6.47
approximately equals 6.47

≈6.14285
approximately equals 6.14285

6.715

1 answer

To convert the mixed number \( 6 \frac{7}{15} \) to a decimal, we first convert it to an improper fraction and then divide.

  1. Convert the mixed number to an improper fraction: \[ 6 \frac{7}{15} = \frac{6 \times 15 + 7}{15} = \frac{90 + 7}{15} = \frac{97}{15} \]

  2. Now we divide \( 97 \) by \( 15 \) using long division.

  • Long Division Steps:
    • \( 15 \) goes into \( 97 \) 6 times (because \( 15 \times 6 = 90 \)).
    • Subtract \( 90 \) from \( 97 \) to get a remainder of \( 7 \).
    • Bring down a \( 0 \) to make \( 70 \).
    • \( 15 \) goes into \( 70 \) 4 times (because \( 15 \times 4 = 60 \)).
    • Subtract \( 60 \) from \( 70 \) to get a remainder of \( 10 \).
    • Bring down another \( 0 \) to make \( 100 \).
    • \( 15 \) goes into \( 100 \) 6 times (because \( 15 \times 6 = 90 \)).
    • Subtract \( 90 \) from \( 100 \) to get a remainder of \( 10 \).
    • Bring down another \( 0 \) to make \( 100 \) again.

This shows that the division will repeat because we keep getting the same remainders. Therefore,

\[ 97 \div 15 = 6.46666... \]

This is approximately \( 6.47 \).

So, the correct answer to convert \( 6 \frac{7}{15} \) into decimal form is: ≈6.47.