Every number that repeats in a predictable pattern, such as 0.Also, 333... Consider this: or 0. 142857142857..., might look endless at first glance, but it is actually a rational number that can be written exactly as a ratio of two integers. Learning how to express the repeating decimal as a fraction in lowest terms is an essential algebra skill that turns an infinite decimal into a clean, simplified fraction. Whether you are working with a single repeating digit or a longer recurring block, the process follows a logical set of steps that removes the repeating portion and leaves you with a numerator and denominator you can reduce to their simplest form.
What Is a Repeating Decimal?
A repeating decimal is a decimal number in which one digit or a group of digits repeats infinitely. That said, mathematicians often indicate this repetition by placing a bar over the repeating digits, known as a vinculum, or by using ellipses (... ) That's the whole idea..
Honestly, this part trips people up more than it should.
- 0.333... can be written as $0.\overline{3}$
- 0.142857142857... can be written as $0.\overline{142857}$
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