In this Grade 7 lesson from Saxon Math Course 2, students learn to identify and write repeating decimals using bar notation over the repetend, distinguishing them from terminating decimals. Students practice converting division problems into repeating decimal form, rounding repeating decimals to a specified number of decimal places, and comparing repeating decimals with terminating decimals. The lesson also introduces how calculators handle repeating decimals through truncation or rounding.
Section 1
📘 Repeating Decimals
Some divisions produce repeating decimals, where one or more digits, called the repetend, repeat in a pattern forever.
One way to indicate that a decimal number has repeating digits is to write the number with a bar over the repetend where it first appears to the right of the decimal point. For example,
This card introduces the core idea. Soon, we'll dive into worked examples on writing, rounding, and comparing these special decimals.
Section 2
Repetend
The repeating digits of a decimal number are called the repetend. We use a bar over the repetend where it first appears to the right of the decimal point to write it concisely.
Think of the bar as a crown for the digits that repeat forever! It’s a super handy shortcut, showing which numbers go on an infinite journey, so you don't have to write them out endlessly.
Section 3
Rounding Repeating Decimals
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.
Round to five decimal places:
Round to five decimal places:
Round to the thousandths place:
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.
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Section 1
📘 Repeating Decimals
Some divisions produce repeating decimals, where one or more digits, called the repetend, repeat in a pattern forever.
One way to indicate that a decimal number has repeating digits is to write the number with a bar over the repetend where it first appears to the right of the decimal point. For example,
This card introduces the core idea. Soon, we'll dive into worked examples on writing, rounding, and comparing these special decimals.
Section 2
Repetend
The repeating digits of a decimal number are called the repetend. We use a bar over the repetend where it first appears to the right of the decimal point to write it concisely.
Think of the bar as a crown for the digits that repeat forever! It’s a super handy shortcut, showing which numbers go on an infinite journey, so you don't have to write them out endlessly.
Section 3
Rounding Repeating Decimals
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.
Round to five decimal places:
Round to five decimal places:
Round to the thousandths place:
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.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter