Decimal Representation of 1/6: A Comprehensive Guide

1/6 is a common fraction that represents a part of a whole. It can be expressed as a decimal by dividing 1 by 6.

Step-by-Step Approach to Find the Decimal for 1/6

1. Set up the division problem: Divide 1 by 6: 1 ÷ 6 = ?

2. Perform long division: Divide the numerator (1) by the denominator (6):

3. Repeat the division: Since the remainder is not zero, continue dividing the remainder (4) by the divisor (6):

4. Observe the pattern: The division repeats itself indefinitely. This means that the decimal for 1/6 is non-terminating and non-repeating.

5. Write the decimal: The decimal for 1/6 is 0.1666... (with the repeating digit 6).

Importance and Benefits of Understanding Decimal Representation

Understanding the decimal representation of fractions is crucial for:

• Accurate mathematical computations, especially in science, engineering, and finance.
• Converting between different fraction forms (e.g., decimals, percentages, ratios).
• Solving real-world problems involving fractions, such as calculating measurements or proportions.

Pros and Cons of Decimal Representation

Pros:

• Easy to use for multiplication, division, and other arithmetic operations.
• Widely accepted and standardized format.
• Convenient for calculations using calculators and computers.

Cons:

• Can be inaccurate or approximate for certain fractions (e.g., 1/3 = 0.333... instead of 0.333).
• May require rounding or truncation for practical purposes.
• Can make it difficult to visualize the original fraction.

FAQs on Decimal Representation of 1/6

1. Is 1/6 a rational or irrational number?
   - 1/6 is a rational number because it can be expressed as a fraction of two integers.

2. How can I find the decimal for 1/6 using a calculator?
   - Enter 1 ÷ 6 into a calculator and press the equals sign to get 0.16666...

3. What is the percentage equivalent of 1/6?
   - 1/6 can be expressed as a percentage by multiplying it by 100, resulting in 16.666...%.

4. How can I convert 1/6 to a decimal without using long division?
   - Multiply both the numerator and denominator by 10 to get 10/60, which can be simplified to 0.16666...

5. Is 1/6 a terminating or repeating decimal?
   - 1/6 is a non-terminating, non-repeating decimal.

6. What is the digit in the tenths place of the decimal for 1/6?
   - The digit in the tenths place is 1.

7. How can I round the decimal for 1/6 to two decimal places?
   - Rounding to two decimal places gives 0.17.

8. Is it possible to find the exact decimal value of 1/6?
   - No, the decimal for 1/6 is an infinite, non-terminating, non-repeating sequence.

Conclusion

Understanding the decimal representation of 1/6 is essential for various mathematical and practical applications. While it can be a non-terminating and non-repeating decimal, it is still a widely used and accurate way of expressing this fraction in a standard format.