Convert the fraction below into a decimal \frac{1}{60}
The correct answer and explanation is:
Decimal Conversion:
160=0.01666‾\frac{1}{60} = 0.0166\overline{6}
This means the decimal is approximately 0.016666…, where the digit 6 repeats infinitely.
Explanation (300 Words):
Converting a fraction into a decimal involves dividing the numerator (top number) by the denominator (bottom number). In the case of the fraction 160\frac{1}{60}, you are dividing 1 by 60.
To perform this division:
1 ÷ 60 = 0.016666…
This decimal is non-terminating and repeating, which means it goes on forever but follows a repeating pattern. In this case, the digit 6 repeats. The notation 0.01666‾0.0166\overline{6} uses a bar over the repeating digit to show that it continues infinitely.
Let’s break it down further:
- The number 60 does not divide evenly into 1, so we must use decimal points and zeros to continue dividing.
- 60 goes into 1 zero times, so we add a decimal point and continue with 10.
- 60 goes into 10 zero times, so we add another 0 and now consider 100.
- 60 goes into 100 once (1 × 60 = 60), with a remainder of 40.
- Bring down a 0, making it 400. 60 goes into 400 six times (6 × 60 = 360), with a remainder of 40.
- Bring down another 0 to get 400 again. This shows that the remainder is repeating, which means the decimal will repeat as well.
This is a repeating decimal, a common result when a fraction’s denominator has a prime factor other than 2 or 5. Since 60 = 2² × 3 × 5, and 3 is not 2 or 5, the decimal repeats.
This also shows why understanding fraction-to-decimal conversions is important—especially in areas like measurements, science, and finance, where precision matters. Knowing that 160=0.01666‾\frac{1}{60} = 0.0166\overline{6} helps when working with recurring decimals or rounding in real-world scenarios.