In this Grade 8 lesson from Saxon Math, Course 3, students learn how to convert fractions and mixed numbers into repeating decimals, identifying the repetend and using bar notation to represent the repeating digits. The lesson covers the three possible outcomes when converting rational numbers to decimal form — integer, terminating decimal, or non-terminating repeating decimal — and distinguishes these from irrational numbers. Students also practice rounding repeating decimals for calculations and comparing decimals such as 0.3, 0.33, and 0.3̄ by ordering them from least to greatest.
Section 1
📘 Repeating Decimals
Fractions can convert to decimals with endlessly repeating digits. We use a bar over this repeating part, called the repetend, to write them efficiently.
The repeating digits are called the repetend. We can indicate repeating digits with a bar over the repetend. We write as .
Section 2
Repetend
The repeating digits in a decimal are called the repetend. We indicate repeating digits with a bar over the repetend, such as writing as .
Some fractions are like a broken record, creating decimals with a repeating pattern. Instead of writing forever, just draw a bar over the part that repeats—the repetend! It's the ultimate math shortcut for 'this goes on and on', keeping your work neat, tidy, and delightfully dramatic.
Section 3
Rational Numbers as Decimals
Converting a rational number to a decimal has three possible outcomes: it becomes an integer, a terminating decimal, or a non-terminating decimal with repeating digits.
Every fraction has a decimal alter-ego! It will either stop cleanly, be a whole number, or repeat a pattern. If a decimal goes on forever without a repeating pattern, it’s not from the rational family—it’s one of those mysterious 'irrational' numbers that doesn't play by the rules.
Section 4
Comparing Repeating Decimals
To arrange repeating decimals in order, write each number out to several decimal places to reveal their true magnitude and allow for an accurate comparison.
A repeating bar can be deceiving! To truly know which decimal is bigger, you must unmask them by writing out their digits side-by-side. Expanding them a few places reveals their actual size, so you can declare a winner without any doubt. It's like a numerical face-off where truth prevails!
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Section 1
📘 Repeating Decimals
Fractions can convert to decimals with endlessly repeating digits. We use a bar over this repeating part, called the repetend, to write them efficiently.
The repeating digits are called the repetend. We can indicate repeating digits with a bar over the repetend. We write as .
Section 2
Repetend
The repeating digits in a decimal are called the repetend. We indicate repeating digits with a bar over the repetend, such as writing as .
Some fractions are like a broken record, creating decimals with a repeating pattern. Instead of writing forever, just draw a bar over the part that repeats—the repetend! It's the ultimate math shortcut for 'this goes on and on', keeping your work neat, tidy, and delightfully dramatic.
Section 3
Rational Numbers as Decimals
Converting a rational number to a decimal has three possible outcomes: it becomes an integer, a terminating decimal, or a non-terminating decimal with repeating digits.
Every fraction has a decimal alter-ego! It will either stop cleanly, be a whole number, or repeat a pattern. If a decimal goes on forever without a repeating pattern, it’s not from the rational family—it’s one of those mysterious 'irrational' numbers that doesn't play by the rules.
Section 4
Comparing Repeating Decimals
To arrange repeating decimals in order, write each number out to several decimal places to reveal their true magnitude and allow for an accurate comparison.
A repeating bar can be deceiving! To truly know which decimal is bigger, you must unmask them by writing out their digits side-by-side. Expanding them a few places reveals their actual size, so you can declare a winner without any doubt. It's like a numerical face-off where truth prevails!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter