Converting Fractions to Decimals
Converting fractions to decimals is done by dividing the numerator by the denominator. For example, 3/5 = 3 divided by 5 = 0.6, and 5/9 = 0.555... (a repeating decimal written as 0.5 with a bar). Mixed numbers like 2 1/4 convert to 2.25. Every fraction of whole numbers produces either a terminating or repeating decimal. This skill is covered in Chapter 5 of Saxon Math Course 2 for 7th grade math and is fundamental for comparing numbers, solving equations, and working with measurements and money.
Key Concepts
Property To change a fraction to a decimal number, we perform the division indicated by the fraction. The fraction $\frac{1}{4}$ indicates that 1 is divided by 4. Every fraction of whole numbers converts to either a terminating decimal or a repeating decimal.
Examples $\frac{3}{5} \rightarrow 3 \div 5 = 0.6$ $\frac{5}{9} \rightarrow 5 \div 9 = 0.555... = 0.\bar{5}$ $2\frac{1}{4} = \frac{9}{4} \rightarrow 9 \div 4 = 2.25$.
Explanation A fraction is just a division problem waiting to happen! To uncover its decimal form, simply divide the top number (numerator) by the bottom number (denominator). You might get a nice, clean answer that stops, called a terminating decimal. Or, you could get a number that repeats forever in a pattern, which we mark with a cool bar on top.
Common Questions
How do you convert a fraction to a decimal?
Divide the numerator by the denominator using long division. For 3/5, divide 3 by 5 to get 0.6. Add zeros after the decimal point in the dividend as needed and continue dividing until the remainder is 0 or a repeating pattern appears.
What is a terminating decimal?
A terminating decimal ends after a finite number of digits, like 0.6 or 2.25. Fractions whose denominators (in simplified form) have only factors of 2 and 5 produce terminating decimals. For example, 3/5 = 0.6 terminates.
What is a repeating decimal?
A repeating decimal has one or more digits that repeat infinitely. For example, 5/9 = 0.555... is written as 0.5 with a bar over the 5. The fraction 1/6 = 0.1666... has the 6 repeating.
How do you convert a mixed number to a decimal?
Convert the fraction part to a decimal, then add the whole number. For 2 1/4: 1 divided by 4 = 0.25, so 2 1/4 = 2.25. Alternatively, convert to an improper fraction first: 9/4 = 2.25.
Which fractions become terminating decimals?
A fraction in lowest terms terminates if and only if the denominator has no prime factors other than 2 and 5. So 1/4 (denominator 4 = 2 x 2) terminates as 0.25, but 1/3 (denominator 3) repeats as 0.333...
When do students learn to convert fractions to decimals?
This conversion skill is introduced in elementary school and practiced extensively in 7th grade math. Saxon Math Course 2 covers it in Chapter 5, where students learn to perform the division and recognize terminating versus repeating results.