What is the decimal form of 5/9?
Understand the Problem
The question is asking for the decimal representation of the fraction 5/9, which can be found by performing the division of 5 by 9.
Answer
The decimal representation of \( \frac{5}{9} \) is \( 0.\overline{5} \).
Answer for screen readers
The decimal representation of ( \frac{5}{9} ) is ( 0.\overline{5} ).
Steps to Solve
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Perform the Division To find the decimal representation of the fraction ( \frac{5}{9} ), we need to divide 5 by 9.
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Set Up the Division Write it as ( 5 \div 9 ). Since 5 is less than 9, we start with 0. We can write it as ( 0. ) and append a decimal point, giving us ( 5.000 \div 9 ).
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Calculate the Decimal Now we can perform the division.
- 9 goes into 50 five times (since ( 9 \times 5 = 45 )).
- Subtract: ( 50 - 45 = 5 ).
- Bring down the next zero, making it 50 again and repeat.
- Identify the Pattern Repeat this division process, and we will see: ( 9 ) goes into ( 50 ) five times, causing a repeating cycle in the decimal. The result is ( 0.5555...), which we can denote with repeating notation as ( 0.\overline{5} ).
The decimal representation of ( \frac{5}{9} ) is ( 0.\overline{5} ).
More Information
The decimal representation ( 0.\overline{5} ) indicates that the digit 5 repeats indefinitely. This is a common result when dividing certain fractions, particularly those with denominators that aren't factors of 10.
Tips
Sometimes, people forget to include the repeating part of the decimal when writing the answer, or they might stop the division too early, thinking it resolves to a finite decimal.
