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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

  1. Set up the division Begin by dividing the numerator (4) by the denominator (9). You can think of this as the long division process.

    $$ 4 \div 9 $$

  2. 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).

  3. Continue Long Division Now divide 40 by 9.

    $$ 9 \text{ goes into } 40 \text{ four times } (9 \times 4 = 36) $$

  4. Calculate the remainder Subtract 36 from 40 to find the remainder:

    $$ 40 - 36 = 4 $$

  5. Bring down another zero Add another zero to the remainder (making it 40 again).

  6. Repeat the division process Repeat the division:

    $$ 9 \text{ goes into } 40 \text{ four times again}, (9 \times 4 = 36) $$

  7. Recognize the pattern You repeat the steps, subtracting 36 from 40 each time, always getting a remainder of 4. Thus, the decimal repeats.

  8. 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.
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