How to write repeating decimals with a bar

Some decimals end, and others go on forever. If a group of digits keeps repeating, we can write the group once and put a bar over it. The bar tells us exactly where the repeat starts.

Separate the part that repeats from the part that comes first

The decimal $32.18476$ terminates because it has a last digit. In $32.184766666 \dots$ , the digits $1847$ come first and then the digit $6$ repeats forever. Put the bar over just the $6$ .

32.184766666 \dots = 32.1847 \bar{6}

A decimal can also go on forever without an eventually repeating pattern. For example, $π$ starts $3.14159265 \dots$ and has no repeating group to mark with a bar.

Put the bar over a group of two digits

In $0.54545454 \dots$ , we see $54$ followed by $54$ again. The pattern starts right after the decimal point, so the bar goes over both digits.

0.54545454 \dots = 0. \bar{54}

A zero can be part of the group too. In $0.07070707 \dots$ , the repeating group is $07$ , so keep both digits under the bar.

0.07070707 \dots = 0. \bar{07}

Learn mathKrista KingAugust 6, 2020math, learn online, online course, online math, pre-algebra, prealgebra, fundamentals of math, math foundations, middle school math, decimals, decimal numbers, repeating decimals

How to write repeating decimals with a bar

Separate the part that repeats from the part that comes first

Put the bar over a group of two digits

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