Rational Numbers as Decimals
Rational Numbers as Decimals is a Grade 7-8 math skill where students learn to convert rational numbers (fractions and integers) into decimal form by dividing the numerator by the denominator. Students identify terminating and repeating decimals and understand that all rational numbers can be expressed as either.
Key Concepts
Property 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.
Examples Integer: The rational number $\frac{12}{4}$ simplifies to the integer $3$. Terminating Decimal: The rational number $\frac{3}{4}$ divides to become the decimal $0.75$. Repeating Decimal: The rational number $\frac{2}{9}$ divides to become the repeating decimal $0.\bar{2}$.
Explanation 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.
Common Questions
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. For example, 3/4 = 3 divided by 4 = 0.75.
What is the difference between a terminating and repeating decimal?
A terminating decimal ends after a finite number of digits (like 0.5 or 0.75). A repeating decimal has a digit or group of digits that repeat forever (like 0.333... for 1/3).
Are all fractions rational numbers?
Yes, any number that can be expressed as a fraction p/q where q is not zero is a rational number, including all integers and fractions.
How do you write a repeating decimal?
Use a bar notation over the repeating digits. For example, 0.333... is written as 0.3 with a bar over the 3.
What grade covers rational numbers as decimals?
Rational numbers as decimals are covered in Grade 7 and Grade 8 math.