Comparing Terminating and Repeating Decimals
Comparing Terminating and Repeating Decimals is a Grade 7 math skill in Reveal Math Accelerated, Unit 13: Irrational Numbers, Exponents, and Scientific Notation, where students classify fractions by whether their decimal equivalents terminate or repeat, and use fraction-to-decimal conversion to compare the sizes of rational numbers expressed in decimal form. This skill supports placing rational numbers on the number line.
Key Concepts
Property To compare terminating and repeating decimals, expand the repeating block for several digits and append zeros to the terminating decimals to match the length. Then, compare the digits from left to right, starting with the greatest place value.
Examples Example 1: Compare 0.45 and $0.\overline{45}$. Expand both decimals to the thousandths place: $0.45 = 0.450...$ $0.\overline{45} = 0.454...$ Comparing the thousandths place, $4 0$, so $0.\overline{45} 0.45$.
Example 2: Order 0.3, 0.33, and $0.\overline{3}$ from least to greatest. Expand the decimals to three decimal places: $0.3 = 0.300...$ $0.33 = 0.330...$ $0.\overline{3} = 0.333...$ Comparing the thousandths place, the correct order is $0.3 < 0.33 < 0.\overline{3}$.
Common Questions
What is the difference between terminating and repeating decimals?
A terminating decimal ends after a finite number of digits (e.g., 0.75). A repeating decimal has one or more digits that repeat forever (e.g., 0.333...). Both types represent rational numbers.
How do you know if a fraction will produce a terminating or repeating decimal?
A fraction in lowest terms produces a terminating decimal if and only if the denominator has no prime factors other than 2 and 5. If the denominator has any other prime factor, the decimal repeats.
How do you compare a terminating and a repeating decimal?
Convert both to the same number of decimal places (rounding the repeating decimal if necessary) or convert both to fractions with a common denominator, then compare their values.
What is Reveal Math Accelerated Unit 13 about?
Unit 13 covers Irrational Numbers, Exponents, and Scientific Notation, including classifying real numbers, comparing rational and irrational numbers, and performing operations with scientific notation.