Fractions to Decimals
Every common fraction can be converted to a decimal by dividing the numerator by the denominator, since the fraction bar means division. The resulting decimal either terminates (ends) like 3/4 = 0.75, or repeats a pattern like 4/9 = 0.444..., written as 0.4 with a bar over the 4. This Grade 8 math skill from Yoshiwara Core Math Chapter 2 builds the number fluency needed to move between fraction and decimal representations, essential for comparing, ordering, and computing with rational numbers. Understanding repeating decimals also introduces students to the concept of irrational numbers and infinite non-repeating decimals.
Key Concepts
Property To convert a common fraction to a decimal, divide the numerator by the denominator. Some decimals terminate (end), while others have a repeating pattern of digits. We use a bar over the repeating digits, for example, $\frac{1}{3} = 0.333... = 0.\overline{3}$.
Examples To convert $\frac{3}{4}$ to a decimal, we calculate $3 \div 4$, which gives $0.75$. This is a terminating decimal. To convert $\frac{4}{9}$ to a decimal, we calculate $4 \div 9$, which gives $0.444...$. We write this repeating decimal as $0.\overline{4}$. The fraction $\frac{5}{12}$ is converted by calculating $5 \div 12 = 0.41666...$. We write this as $0.41\overline{6}$, with the bar only over the repeating digit.
Explanation A fraction is just a division problem in disguise! When you perform the division, the answer is its decimal form. It either stops neatly (terminates) or repeats a pattern forever.
Common Questions
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. The fraction bar means division. For example, 3/4 = 3 divided by 4 = 0.75. You can do this by hand or with a calculator.
What is a terminating decimal?
A terminating decimal is a decimal that ends after a finite number of digits. For example, 1/4 = 0.25 and 3/8 = 0.375 are terminating decimals. Fractions with denominators that are products of only 2s and 5s produce terminating decimals.
What is a repeating decimal?
A repeating decimal is a decimal where a digit or group of digits repeats infinitely. For example, 1/3 = 0.333... and 5/12 = 0.41666... We use a bar over the repeating digit(s) to write them compactly.
When do 8th graders learn to convert fractions to decimals?
Students study fraction-to-decimal conversion in Grade 8 math as part of Chapter 2 of Yoshiwara Core Math, which covers numbers and variables including fraction and decimal relationships.
How do you write a repeating decimal using bar notation?
Place a bar over the digit or group of digits that repeats. For example, 2/3 = 0.666... is written as 0.6 with a bar over the 6. The number 5/12 = 0.41666... is written as 0.41 with a bar only over the final 6.
How do fractions to decimals relate to percent?
Percents are just fractions with denominator 100. Converting a fraction to a decimal is the same as finding its decimal, and multiplying that by 100 gives the percent. For example, 3/4 = 0.75 = 75%.