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Use long division to convert the rational number 4/9


to its equivalent decimal form

5 answers

To convert the rational number \( \frac{4}{9} \) to its equivalent decimal form using long division, we can follow these steps:

  1. Set up the division: We want to divide 4 by 9. Since 4 is less than 9, we can write this as \( 4.000000 \div 9 \).

  2. Perform the long division:

    • Step 1: 9 goes into 40 (the first two digits of 4.000000) 4 times, since \( 9 \times 4 = 36 \). Write 4 above the line.
    • Step 2: Subtract 36 from 40, which gives us 4. Bring down the next 0 to make it 40 again.
    • Step 3: Repeat the process. 9 goes into 40, again, 4 times. Subtract 36 from 40 to get 4, then bring down the next 0.

  3. Recognizing the pattern: You will notice that the remainder is 4 every time you bring down a 0. This means that the process will repeat indefinitely.

The division looks like this:

      0.44444...
    __________
9 | 4.000000...
     -36
     ----
      40
     -36
     ----
      40
     -36
     ----
      40
     ...
  1. Conclusion: The decimal representation of \( \frac{4}{9} \) is \( 0.4\overline{4} \), where the \( 4 \) repeats indefinitely.

So, the equivalent decimal form of \( \frac{4}{9} \) is:

\[ 0.44444\ldots \text{ or } 0.4\overline{4} \]

can you do it without all the symbols and slashes
and can you do lees words and make it more advanced

Certainly!

To convert \(4 \div 9\) into decimal form using long division:

  1. Setup: Divide 4.000000 by 9.

  2. First Iteration:

    • 9 goes into 40 four times (4).
    • \(9 \times 4 = 36\).
    • Subtract: \(40 - 36 = 4\).
    • Bring down the next 0, making it 40 again.

  3. Subsequent Iterations:

    • Repeat: 9 into 40 is again 4, giving us the same calculations.
    • The remainder is always 4, repeating indefinitely.

Result: The decimal representation of \( \frac{4}{9} \) is \(0.4\) with 4 repeating, denoted as \(0.\overline{4}\).

can you do it without all the slashes and symbols

Sure! Here is a concise version without slashes or symbols:

To convert four divided by nine into a decimal using long division:

  1. Set up the division with four as the dividend and nine as the divisor.
  2. Nine goes into forty four times.
  3. Multiply four by nine to get thirty-six.
  4. Subtract thirty-six from forty, which leaves four.
  5. Bring down a zero, making it forty again.
  6. Repeat the process: nine goes into forty four times, leaving a remainder of four each time.

This results in a repeating decimal. Therefore, the decimal form of four divided by nine is zero point four, with the four repeating indefinitely.