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

Question

Responses

4.15
4.15

3.75
3.75

≈0.27
approximately equals 0.27

26
26

Answer 1

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

1. Set up the long division: Divide 4 (the numerator) by 15 (the denominator). Since 4 is less than 15, you start with 0.
2. Add decimal places: Add a decimal point and zeros to the dividend (4.000...).
3. Divide:
   • How many times does 15 go into 40? It goes 2 times (because \( 15 \times 2 = 30 \)).
   • Write 2 above the line.
   • Subtract \( 30 \) from \( 40 \) to get \( 10 \).
4. Bring down the next zero: Bringing down another zero makes it \( 100 \).
5. Repeat the process:
   • How many times does 15 go into \( 100 \)? It goes 6 times (because \( 15 \times 6 = 90 \)).
   • Write 6 above the line next to 2.
   • Subtract \( 90 \) from \( 100 \) to get \( 10 \).
6. Bring down another zero, and you again have \( 100 \).
7. Repeat the division: You'll again get 6, and this process will repeat indefinitely.

Thus, the decimal is: \[ 0.2666...\] or approximately: \[ 0.27\]

So the correct answer is: ≈0.27.