Select the decimal that is equivalent to \[\dfrac{57}{220}\]

General
1

select the decimal that is equivalent to [\dfrac{57}{220}].

2

Select the decimal that is equivalent to (\dfrac{57}{220})

Answer: To find the decimal equivalent of (\dfrac{57}{220}), we need to perform division where 57 is the dividend and 220 is the divisor.

Let’s break down the division step-by-step:

  1. Set Up the Division:

    • We place 57 under the division symbol (the dividend) and 220 the outside (the divisor).

  2. Perform the Division:

    • We first consider if 220 fits into 57. Since 57 is smaller than 220, we determine how many times 220 fits into a larger placeholder, starting by looking at 570 (by adding a decimal place and zero).

  3. Calculate the Initial Steps:

    • Calculate (570 \div 220): 220 fits into 570 approximately 2 times, since (220 \times 2 = 440).
    • Subtract 440 from 570 which gives 130.

  4. Bring Down the Next Placeholder:

    • Bring down the next zero, turning 130 to 1300.

  5. Continue the Process:

    • Calculate (1300 \div 220): 220 fits into 1300 about 5 times, since (220 \times 5 = 1100).
    • Subtract 1100 from 1300 to get 200.

  6. Proceed Further in Division:

    • Bring down another zero to make it 2000.
    • Calculate (2000 \div 220): 220 fits into 2000 approximately 9 times, since (220 \times 9 = 1980).
    • Subtract 1980 from 2000 to get 20.

  7. Final Calculations for Precision:

    • Continue with the division by bringing down another zero making it 200 (as zero was already considered after decimal point initiation).
    • 220 again does not fit into 200, so consider it as convergence for this stage of approximation.

Finally, the division yields a repeating decimal, represented by 0.259 repeating.

0.2590909090...
  1. Rounding for Simplification:
    • Given that decimals generally might be requested to a specified number of decimal places, (\dfrac{57}{220} \approx 0.259) when rounded to three decimal places.

In summary, the equivalent decimal of the fraction (\dfrac{57}{220}) is approximately 0.259 when rounded for simplicity, though it technically continues as a repeating decimal with digits “0909”.

@anonymous6