Rounding Repeating Decimals
Rounding repeating decimals requires first writing out the repeating pattern past the desired place value, then applying standard rounding rules. For example, to round 5.31 repeating 6 to five decimal places, write 5.316666... and round to 5.31667. To round 0.888... to the thousandths place, write 0.8888 and round to 0.889. This technique is taught in Chapter 5 of Saxon Math Course 2 and helps 7th grade students handle the repeating decimals that arise from fraction-to-decimal conversions.
Key Concepts
Property To round a repeating decimal, first remove the bar and write out the repeating pattern past the desired place value. Then, you can apply standard rounding rules to the newly expanded number.
Examples Round $5.31\overline{6}$ to five decimal places: $5.316666... \rightarrow 5.31667$ Round $25.\overline{405}$ to five decimal places: $25.405405... \rightarrow 25.40541$ Round $0.\overline{8}$ to the thousandths place: $0.8888... \rightarrow 0.889$.
Explanation You can't round a number that's still hiding its true self! First, un repeat the decimal by writing it out long form. After you see the full number, you can round it up or down like any other.
Common Questions
How do you round a repeating decimal?
Expand the repeating pattern past the place value you are rounding to, then apply normal rounding rules. For 0.833... rounded to hundredths, write 0.833 and round to 0.83.
What is a repeating decimal?
A repeating decimal has one or more digits that repeat infinitely, such as 0.333... (1/3) or 0.142857142857... (1/7). A bar over the repeating digits shows the pattern.
How do you round 0.888... to the thousandths place?
Write out enough digits: 0.8888. The thousandths digit is 8 and the next digit is 8, so round up to 0.889.
Why do repeating decimals occur?
Repeating decimals occur when dividing by a number whose prime factors include something other than 2 or 5. For example, 1/3 = 0.333... because 3 is not a factor of 10.
What are common mistakes when rounding repeating decimals?
Students sometimes round based on the bar notation without expanding the digits, which can lead to rounding the wrong digit. Always write out the pattern past the target place.
Is rounding repeating decimals part of 7th grade math?
Yes. Saxon Math Course 2 teaches this skill in Chapter 5, connecting repeating decimal concepts with practical rounding.