What is 5/9 written as a decimal?
The correct answer and explanation is:
The fraction 59\frac{5}{9} written as a decimal is approximately 0.5555…, which is a repeating decimal often written as 0.\overline{5}.
How to Convert 59\frac{5}{9} to a Decimal
To convert a fraction like 59\frac{5}{9} into a decimal, you divide the numerator (top number) by the denominator (bottom number):
- Divide 5 by 9.
Performing the division:
- 9 goes into 5 zero times, so start with 0.
- Put a decimal point and add a zero, making it 50.
- 9 goes into 50 five times (because 9×5=459 \times 5 = 45), so the first decimal digit is 5.
- Subtract 45 from 50, leaving a remainder of 5.
- Bring down another zero, making 50 again.
- Repeat the process: 9 goes into 50 five times, remainder 5.
- This process repeats infinitely.
Because the remainder keeps repeating as 5, the decimal digit 5 repeats endlessly. This means the decimal is 0.5555…, a repeating decimal.
Explanation of Repeating Decimals
When a fraction’s denominator has factors other than 2 or 5, its decimal representation often repeats. This happens because in division, the remainders cycle through the same values, leading to repeated digits.
In the case of 59\frac{5}{9}:
- The denominator 9 is a factor of 3².
- Fractions with denominators like 3, 9, 27, etc., have repeating decimals.
- 19=0.1‾\frac{1}{9} = 0.\overline{1}
- 59\frac{5}{9} is simply 5 times 19\frac{1}{9}, so the decimal repeats 5 indefinitely.
Summary
- 59=0.5‾\frac{5}{9} = 0.\overline{5}
- The decimal repeats the digit 5 infinitely.
- This is because dividing 5 by 9 results in a remainder that repeats, producing a repeating decimal.
So, the exact decimal form of 59\frac{5}{9} is a repeating decimal 0.5555…, often denoted as 0.\overline{5}.