Write 5/6 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
Understand the Problem
The question is asking how to convert the fraction 5/6 into a decimal form. It also specifies to indicate if there are repeating digits using a bar notation.
Answer
$0.83\overline{3}$
Answer for screen readers
The decimal form of $\frac{5}{6}$ is $0.83\overline{3}$.
Steps to Solve
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Set up the division To convert the fraction $\frac{5}{6}$ into decimal form, we need to perform the division of 5 by 6.
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Perform the long division Divide 5 by 6. Since 5 is less than 6, we start by adding a decimal point and a zero, making it 50.
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Calculate the first digit after the decimal point $6$ goes into $50$ $8$ times, since $8 \times 6 = 48$. Subtract $48$ from $50$: $$ 50 - 48 = 2 $$
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Bring down the next zero Now, bring down another zero making it 20. Now, we divide: $6$ goes into $20$ $3$ times, since $3 \times 6 = 18$. Subtract $18$ from $20$: $$ 20 - 18 = 2 $$
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Repeat the process Bring down another zero making it 20 again. We see this process will repeat: $6$ goes into $20$ $3$ times, leaving $2$ again.
This gives a repeating decimal representation.
- Final representation Since the digit $3$ repeats, we can write the answer as $0.83\overline{3}$.
The decimal form of $\frac{5}{6}$ is $0.83\overline{3}$.
More Information
The decimal representation $0.83\overline{3}$ indicates that the digit $3$ repeats indefinitely. This type of conversion between fractions and decimals is common in mathematics, especially when dealing with rational numbers.
Tips
- Confusing the remainder with the decimal representation. Ensure to understand that if the same remainder appears again, the decimal will start repeating.
- Incorrectly placing the decimal point or failing to add zeros when necessary. Always keep track of decimal shifts during long division.
