1/6 is what decimal? A Comprehensive Guide to Fractions and Decimals

Understanding the relationship between fractions and decimals is essential for mathematical proficiency. In this comprehensive guide, we will delve into the conversion of 1/6 to decimal form, exploring its significance, applications, and common misunderstandings.

1/6 as a Decimal: Meaning and Significance

The fraction 1/6 represents one part out of six equal parts of a whole. To convert it to a decimal, we divide the numerator (1) by the denominator (6):

1 ÷ 6 = 0.16666...

This result is a non-terminating decimal, meaning it has an infinite number of digits. However, we can round it up to a certain decimal place for practical purposes. For example, to three decimal places, 1/6 is approximately equal to 0.167.

Applications of 1/6 in Decimal Form

The decimal form of 1/6 has numerous applications in various fields:

• Geometry: It represents the ratio of the height to the width of an equilateral triangle.
• Physics: It is used to calculate the coefficient of restitution for objects in collision.
• Finance: It represents a 16.67% interest rate or a 16.67% share of a portfolio.
• Probability: It represents the probability of rolling a '4' or '6' on a standard six-sided die.

Conversion Table: Fractions to Decimals

For quick reference, here is a table of common fractions and their corresponding decimal equivalents:

Common Mistakes to Avoid

When working with fractions and decimals, it is important to avoid the following common mistakes:

• Rounding errors: Always round decimal results to a reasonable number of decimal places, depending on the context.
• Misinterpreting non-terminating decimals: Understand that non-terminating decimals are an approximation of the actual value.
• Confusing fractions and decimals: Remember that fractions and decimals are different ways of representing the same numerical value.

Step-by-Step Approach to Fraction-to-Decimal Conversion

To convert any fraction to a decimal, follow these steps:

1. Divide the numerator by the denominator using long division or a calculator.
2. Check if the decimal terminates or is non-terminating.
3. Round the result to the desired number of decimal places.

Stories and Lessons Learned

Story 1:

A pizza is cut into six equal slices. John eats two slices. What fraction of the pizza has he eaten?

Lesson: 1/6 represents the size of each slice, so John has eaten 2/6 or 1/3 of the pizza.

Story 2:

A basketball team has a 60% winning percentage. What is this percentage as a decimal?

Lesson: A percentage is a fraction out of 100, so 60% can be expressed as 60/100, which is equivalent to 0.6 as a decimal.

Story 3:

A store offers a discount of 15%. If a shirt originally costs $50, what is the discounted price?

Lesson: A discount of 15% is equivalent to 0.15 as a decimal. The discounted price is calculated as $50 - ($50 * 0.15) = $42.50.

Tips and Tricks

• Use a fraction calculator: Online calculators can quickly convert fractions to decimals and vice versa.
• Estimate the decimal: For approximate calculations, round the fraction to a simpler form (e.g., 1/6 to 1/5 or 0.2) and convert the rounded fraction to a decimal.
• Memorize common conversions: Remember the decimal equivalents of common fractions, such as 1/2 (0.5), 1/4 (0.25), and 1/8 (0.125).

Authoritative Sources

• National Council of Teachers of Mathematics (NCTM): https://www.nctm.org/
• Mathematical Association of America (MAA): https://www.maa.org/
• United States Department of Education: https://www.ed.gov/