6 Questions
What is a characteristic of an irrational number?
It has a non-terminating and non-repeating decimal expansion
What is the purpose of finding the simplest form of a fraction?
To eliminate any common factors between the numerator and denominator
What is a repeating decimal?
A decimal that has a sequence of digits that repeats indefinitely
What is the purpose of ratios?
To compare two quantities and describe their proportions and rates
What is an equivalent ratio?
A ratio that has the same value as the original ratio, but a different form
What is a terminating decimal?
A decimal that ends after a finite number of digits
Study Notes
Rational Numbers
Irrational Numbers
- A number that cannot be expressed as a finite decimal or fraction
- Examples: π, e, √2
- Cannot be written in the form a/b, where a and b are integers and b ≠ 0
- Non-terminating and non-repeating decimal expansion
Fractions
- A way to represent a rational number as a quotient of two integers
- Form: a/b, where a is the numerator and b is the denominator
- Equivalent fractions: fractions that have the same value, but different forms
- Simplest form: a fraction in which the numerator and denominator have no common factors
Decimals
- A way to represent a rational number in base 10
- Terminating decimal: a decimal that ends after a finite number of digits
- Repeating decimal: a decimal that has a sequence of digits that repeats indefinitely
- Converting fractions to decimals: dividing the numerator by the denominator
Ratios
- A comparison of two quantities
- Form: a:b or a/b, where a and b are quantities being compared
- Equivalent ratios: ratios that have the same value, but different forms
- Used to describe proportions and rates
Test your understanding of rational numbers, including irrational numbers, fractions, decimals, and ratios. Learn how to represent and manipulate these numbers in different forms.
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