Curriculum placement
Grade 8. This describes the skill, not a learner estimate.
Telling rationals from irrationals
Distinguish rational numbers from irrational numbers
Problem types
- Select the rational numbers among roots and powers
- Rational or irrational
- Repeating decimals as fractions
Builds on
- Fluent decimal arithmetic
- A fraction as division
- Fluent whole-number division · Useful idea
Dividing the numerator by the denominator turns a fraction into a decimal. Rational numbers give decimals that end or repeat.
Leads to
- Approximating roots
- Which number systems stay closed
- Calculating with complex numbers · Extend the idea
Adding irrational numbers to the rationals gives the real numbers, and complex numbers extend them again to solve x squared = -1.
Related skills
- Decimal place value through thousandths · Related idea
A rational number has a decimal that ends or repeats, and irrational numbers have decimals that do neither, which place value helps classify.
- Tenths and hundredths as decimals · Related idea
Every fraction has a decimal name that ends or repeats, and a repeating decimal is converted back to a fraction.
- Understanding ratios · Shared foundations
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