Question
Write \( \frac{5}{18} \) as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
Ask by Burgess Bradley. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \frac{5}{18} \) as a decimal is \( 0.\overline{27} \).
Solution
To convert 5/18 to a decimal, divide 5 by 18:
• 18 goes into 5 zero times, so write down 0.
• Put a decimal point and bring down a 0 (making it 50).
• 18 goes into 50 two times (2 × 18 = 36) with a remainder of 50 − 36 = 14.
• Bring down another 0 (making it 140). 18 goes into 140 seven times (7 × 18 = 126) with a remainder of 140 − 126 = 14.
• Since the remainder 14 is repeating, the digit 7 will repeat indefinitely.
Thus, the decimal representation of 5/18 is 0.2̅7, where the bar indicates that the digit 7 repeats.
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Extra Insights
To convert \( \frac{5}{18} \) to a decimal, you can perform the division of 5 by 18. When you do the division, you find that \( 5 \div 18 \) equals approximately 0.2777..., where the digit 7 repeats indefinitely. Thus, in decimal form, \( \frac{5}{18} \) can be written as \( 0.2\overline{7} \).