Repeating Decimals as Fractions, Longer Repeats

Start with the division sheet so students see where repeating decimals come from. Teach the 10x method with the one digit sheet before moving to longer repeats.

Turn longer repeats such as 0.363636… and delayed repeats such as 0.2555… into fractions. The bar covers only the repeating digits, so 0.2 5 is 0.2555… while 0. The directions on the page read: Let x equal the decimal. Multiply x by powers of 10 to get two numbers with the same digits after the decimal point. Subtract, solve for x, and write x in simplest form. An answer key is included.

Yes, both. We made it for 8th grade number theory, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

Divide the numerator by the denominator. If the division ends, as with 3/8 = 0.375, the decimal terminates. If a digit or block keeps coming back, as with 7/11, it repeats, and you draw a bar over the repeating digits.

Let x = 0.444…, so 10x = 4.444…. Subtract x from 10x to get 9x = 4, so x = 4/9. Write Repeating Decimals as Fractions uses this 10x method for 10 decimals.

Multiply by a larger power of 10 so the repeating digits line up, such as 100x for 0.363636…. If the repeat starts later, as in 0.2555…, use two powers of 10 so the digits after the decimal point match. Repeating Decimals as Fractions, Longer Repeats has eight of these.