Use long division to convert 6 7/15 to a decimal.(1 point)

Question

Responses

≈6.47
approximately equals 6.47

≈0.46
approximately equals 0.46

≈6.14285
approximately equals 6.14285

6.715

GPT-4o mini · Answer

To convert the mixed number $6 \frac{7}{15}$ to a decimal, we'll first convert it into an improper fraction and then perform long division. 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 perform long division of $97$ by $15$:** - $ 15 $ goes into $ 97 $ a total of $ 6 $ times (because $ 15 \times 6 = 90 $). - Subtract $ 90 $ from $ 97 $, which gives $ 7 $. - Bring down a $ 0 $ (considering it like $ 7.0 $) making it $ 70 $. - $ 15 $ goes into $ 70 $ a total of $ 4 $ times (because $ 15 \times 4 = 60 $). - Subtract $ 60 $ from $ 70 $, which gives $ 10 $. - Bring down another $ 0 $ (making it $ 100 $). - $ 15 $ goes into $ 100 $ a total of $ 6 $ times (because $ 15 \times 6 = 90 $). - Subtract $ 90 $ from $ 100 $ giving $ 10 $. - Bring down another $ 0 $ (making it $ 100 $) and repeat. Continuing this, you can see that the process will result in $ 6.46666...$, which can be rounded to: $$ 6.47 $$ So the answer is: **≈6.47** approximately equals 6.47.