Frequently Asked Questions
Everything you need to know about Repeating Decimal Fractions
What is a repeating decimal and how do you identify one?
+ A repeating decimal is a number where digits after the decimal point repeat infinitely in a periodic pattern. For example, 0.454545... where 45 repeats continuously. You can identify them when performing long division and the same remainder appears again, creating a cycle.
How do you convert a fraction to a repeating decimal step by step?
+ Follow these steps: 1) Write the fraction as a long division problem, 2) Add a decimal point and several zeros to the dividend, 3) Perform the division copying the decimal point to the quotient, 4) Add ellipses (...) to show the pattern continues infinitely.
Which fractions create repeating decimals instead of terminating ones?
+ Fractions whose denominators cannot be converted to powers of 10 (like 100, 1000, 10000) through multiplication create repeating decimals. Examples include fractions with denominators like 3, 6, 7, 9, 11, 12, and 13.
Why does 2/9 equal 0.222... as a repeating decimal?
+ When dividing 2 by 9 using long division, you get remainder 2 repeatedly. This creates the pattern: 2÷9 = 0.2, then 20÷9 = 2 remainder 2, then 20÷9 = 2 remainder 2 again, continuing infinitely as 0.222...
What's the difference between 0.5 and 0.333... in decimal notation?
+ 0.5 is a terminating decimal that ends after one digit, while 0.333... is a repeating decimal where the digit 3 continues infinitely. Terminating decimals have exact decimal representations, while repeating decimals require ellipses (...) to show continuation.
How many zeros should you add when converting fractions to decimals?
+ Add about 5 zeros after the decimal point when starting the long division process. This gives you enough digits to identify the repeating pattern. You can add more zeros if needed to confirm the pattern repeats consistently.
Can you predict if a fraction will be repeating without doing division?
+ Yes! Reduce the fraction to lowest terms first. If the denominator has only factors of 2 and 5, it terminates. If the denominator has any other prime factors (like 3, 7, 11), it will be repeating.
What does the remainder tell you in repeating decimal division?
+ The remainder is key to identifying repeating patterns. When the same remainder appears again during long division, the decimal will start repeating from that point. For example, in 2/11 = 0.181818..., remainders 2 and 9 alternate continuously.