Rational Numbers and Decimals
Rational Numbers and Decimals is a Grade 8 math skill in Saxon Math Course 3, Chapter 7, teaching students that every rational number converts to either a terminating or repeating decimal. Students practice long division to convert fractions to decimals, use bar notation to represent repeating decimals, and compare values across fraction, decimal, and percent forms.
Key Concepts
Property A rational number converted to a decimal either terminates (ends) or repeats forever. A repeating decimal is shown with a bar, like $\frac{1}{11} = 0.\overline{09}$.
Examples $\frac{2}{3}$ is the repeating decimal $0.\bar{6}$, which rounds to $0.667$. To compare $\frac{4}{5}$, $83\frac{1}{3}\%$, and $0.83$, convert them to decimals: $0.800$, $0.833$, $0.830$. The fraction $\frac{1}{8}$ is a terminating decimal, $0.125$.
Explanation That repeating bar means the decimal goes on forever! For precise math, it’s best to use the original fraction in your calculations. Only round your final answer if needed, otherwise you might introduce small but sneaky errors into your work!
Common Questions
What is the difference between a terminating and a repeating decimal?
A terminating decimal ends after a finite number of digits, such as 0.75. A repeating decimal has a digit or group of digits that repeats forever, written with a bar over the repeating part.
How do you convert a fraction to a decimal in Grade 8?
Divide the numerator by the denominator using long division. If the remainder reaches zero the decimal terminates; if a remainder repeats the decimal repeats.
What does the bar over a decimal mean?
The bar notation placed over one or more digits indicates those digits repeat infinitely. For example 0.36 with a bar means 363636 continuing forever.
Are all rational numbers either terminating or repeating decimals?
Yes. Every rational number expressed as a fraction of two integers will produce a decimal that either terminates or eventually repeats a pattern.
Which textbook covers rational numbers and decimals for Grade 8?
This topic is covered in Saxon Math Course 3, Chapter 7: Algebra, a common Grade 8 curriculum resource.