How do you write 4/9 as a decimal?
Understand the Problem
The question is asking how to convert the fraction 4/9 into its decimal form. This involves dividing the numerator (4) by the denominator (9) to get the decimal equivalent.
Answer
The decimal equivalent of the fraction $\frac{4}{9}$ is $0.\overline{4}$.
Answer for screen readers
The decimal equivalent of the fraction $\frac{4}{9}$ is $0.\overline{4}$.
Steps to Solve
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Set up the division Begin by dividing the numerator (4) by the denominator (9). You can think of this as the long division process.
$$ 4 \div 9 $$
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Perform the division Since 4 is less than 9, the whole number part of the answer is 0. Place a decimal point and add a zero to the dividend (making it 40).
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Continue Long Division Now divide 40 by 9.
$$ 9 \text{ goes into } 40 \text{ four times } (9 \times 4 = 36) $$
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Calculate the remainder Subtract 36 from 40 to find the remainder:
$$ 40 - 36 = 4 $$
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Bring down another zero Add another zero to the remainder (making it 40 again).
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Repeat the division process Repeat the division:
$$ 9 \text{ goes into } 40 \text{ four times again}, (9 \times 4 = 36) $$
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Recognize the pattern You repeat the steps, subtracting 36 from 40 each time, always getting a remainder of 4. Thus, the decimal repeats.
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Write the final answer Since the division repeats, we can express it as $0.\overline{4}$, indicating that the digit 4 repeats indefinitely.
The decimal equivalent of the fraction $\frac{4}{9}$ is $0.\overline{4}$.
More Information
When converting fractions to decimals, it's important to identify if the decimal will terminate or repeat. The fraction $\frac{4}{9}$ has a repeating decimal, which can be represented by the overline notation.
Tips
- A common mistake is to forget to add a decimal point and zero when dividing. Remember to do this when the numerator is less than the denominator.
- Another mistake is to assume the division stops when it doesn't; always check for patterns in the remainders.
