Question

Use long division to convert 4/15 to a decimal.(1 point)
Responses

3.75
3.75

≈0.27
approximately equals 0.27

4.15
4.15

26

Answer 1

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Answer 2

To convert \( \frac{4}{15} \) to a decimal using long division, we can follow these steps:

1. Set up the long division by dividing 4 by 15.
2. Since 15 cannot go into 4, we add a decimal point and a zero, making it 40.
3. 15 goes into 40 two times (since \( 15 \times 2 = 30 \)).
4. Subtract 30 from 40, which leaves us with 10.
5. Bring down another zero (making it 100).
6. 15 goes into 100 six times (since \( 15 \times 6 = 90 \)).
7. Subtract 90 from 100, which leaves us with 10.
8. Bring down another zero (making it 100).
9. Repeat the steps: 15 goes into 100 six times, again.

At this point, you'll notice that the process will repeat, producing a recurring decimal.

Thus, \( \frac{4}{15} \) is approximately \( 0.2666... \), which can also be written as \( 0.27 \) when rounded to two decimal places.

The correct response is: **approximately equals 0.27**.

Answer 3

Yes, I am sure! When you perform long division for \( \frac{4}{15} \):

1. Start dividing 4 by 15.
2. 15 goes into 40 two times, which gives you 30. Subtracting 30 from 40 leaves you with 10.
3. Bring down another 0 to make it 100.
4. 15 goes into 100 six times, which gives you 90. Subtracting 90 from 100 leaves you with 10 again.
5. Bring down another 0, and this repeats.

This results in a recurring decimal of \( 0.26666... \), which is often rounded to \( 0.27 \).

So the decimal equivalent of \( \frac{4}{15} \) is indeed approximately \( 0.27 \).