Thirds as decimals and percents
The fractions 1/3 and 2/3 produce repeating decimals that never terminate: 1/3 = 0.333... and 2/3 = 0.666..., written with bar notation as 0.3 bar and 0.6 bar. Their exact percent forms are 33 1/3% and 66 2/3%. This Grade 8 math skill from Yoshiwara Core Math Chapter 2 teaches students to work precisely with fractions that cannot be converted to clean decimals. Using the mixed-number percent form (33 1/3%) instead of the approximation 33% prevents rounding errors in calculations involving thirds, a common requirement in finance, measurement, and everyday problem-solving.
Key Concepts
Property The fraction $\frac{1}{3}$ has a repeating decimal form: $0.333...$ or $0.\overline{3}$. We often approximate it as $0.33$. The exact percent form is $33\frac{1}{3}\%$. For $\frac{2}{3}$, the decimal is $0.666...$ or $0.\overline{6}$, and the exact percent is $66\frac{2}{3}\%$.
Examples A baker needs to find $\frac{1}{3}$ of a 150 pound bag of flour. This is $150 \div 3 = 50$ pounds. This is exactly $33\frac{1}{3}\%$ of the bag. To find $66\frac{2}{3}\%$ of 90 dollars, recognize this percent as the fraction $\frac{2}{3}$. The amount is $\frac{2}{3} \times 90 = 2 \times (90 \div 3) = 2 \times 30 = 60$ dollars. A project is estimated to take 12 hours. If you have completed $\frac{1}{3}$ of the work, you have worked $12 \div 3 = 4$ hours. The decimal representation is approximately $0.33$ of the total time.
Explanation Not all fractions have clean decimal endings. Thirds are a classic example of repeating decimals. Using mixed number percents like $33\frac{1}{3}\%$ allows for perfect accuracy without rounding, which is important in many calculations.
Common Questions
What is 1/3 as a decimal?
1/3 as a decimal is 0.333... (a repeating decimal). The digit 3 repeats infinitely. It is written in bar notation as 0.3 with a bar over the 3. For approximate calculations, 0.33 is often used.
What is 1/3 as a percent?
1/3 as a percent is exactly 33 1/3 percent. This is more precise than saying 33 percent. If you need an exact answer, use 33 1/3 percent rather than rounding.
What is 2/3 as a decimal and percent?
2/3 as a decimal is 0.666... (repeating), written as 0.6 with a bar over the 6. As a percent, 2/3 = 66 2/3 percent exactly.
When do 8th graders learn about thirds as decimals and percents?
Students study thirds in decimal and percent form in Grade 8 math as part of Chapter 2 of Yoshiwara Core Math, which covers numbers and variables including decimal and percent conversions.
Why do thirds produce repeating decimals?
A fraction produces a terminating decimal only when its denominator has no prime factors other than 2 and 5. Since 3 has neither 2 nor 5 as a factor, 1/3 produces a repeating decimal.
How do you calculate 66 2/3% of a number?
Recognize 66 2/3% as 2/3. Then find 2/3 of the number by dividing by 3 and multiplying by 2. For example, 66 2/3% of 90 = 2/3 x 90 = 60.