To convert the fraction \( \frac{4}{15} \) to a decimal using long division, follow these steps:
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Set up the division: You're dividing 4 by 15.
\[ 4 ÷ 15 \]
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Since 4 is less than 15, you will add a decimal point and zeros to continue the division. Rewrite 4 as 4.000. Now you are calculating \( 40.00 ÷ 15 \).
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Perform the long division:
- 15 goes into 40: 2 times (because \( 15 \times 2 = 30 \)).
- Subtract: \( 40 - 30 = 10 \).
- Bring down the next 0: Now you have 100.
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Continue dividing:
- 15 goes into 100: 6 times (because \( 15 \times 6 = 90 \)).
- Subtract: \( 100 - 90 = 10 \).
- Bring down the next 0: Now you have 100 again.
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Repeat:
- 15 goes into 100: 6 times (again).
- Subtract: \( 100 - 90 = 10 \).
- Bring down the next 0: You will see that it will again yield 100.
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It becomes apparent that the pattern will repeat. Each time you perform the division from \( 100 \), you'll get 6 with a remainder of 10, leading to another 100.
So, the decimal representation of \( \frac{4}{15} \) is:
\[ 0.2666... \]
This can also be noted as \( 0.2\overline{6} \), indicating that the digit 6 repeats indefinitely. Thus:
\[ \frac{4}{15} = 0.26666... \]
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