The number system rational and irrational numbers quick check 8th grade
Here is the quick check for 8th grade on the number system, specifically rational and irrational numbers:
1. Classify the following numbers as either rational or irrational:
a) 3.5 - Rational
b) √5 - Irrational
c) 0.75 - Rational
d) π - Irrational
e) 0.333333... - Rational (repeating decimal)
2. Determine if the given statement is true or false:
a) Irrational numbers cannot be written as fractions. - True
b) Rational numbers can be written as terminating decimals or repeating decimals. - True
c) Every square root is an irrational number. - False (some square roots are rational)
d) Zero is considered an irrational number. - False (zero is considered a rational number)
3. Simplify the following expressions:
a) √9 + √16 - 5
Simplifying each square root:
3 + 4 - 5 = 2
b) (4√2 - √8)(2 + √2)
Simplifying each square root:
(4√2 - 2√2)(2 + √2)
2√2(2 + √2)
4√2 + 2√2√2
4√2 + 4
4(√2 + 1)
These questions cover the basic concepts of rational and irrational numbers at an 8th-grade level. Make sure to review the definitions and properties of these types of numbers to have a solid understanding.
Sure! Here's a step-by-step explanation of rational and irrational numbers:
1. Rational numbers:
- Rational numbers are numbers that can be expressed as fractions or ratios of two integers.
- They can be written in the form a/b, where a and b are integers, and b is not equal to zero.
- Examples of rational numbers include 1/2, -5/3, 6, and -3.
2. Irrational numbers:
- Irrational numbers are numbers that cannot be expressed as fractions or ratios of two integers.
- They cannot be written in the form a/b, where a and b are integers. Instead, they are non-repeating and non-terminating decimals.
- Examples of irrational numbers include √2, π (pi), and e (the base of the natural logarithm).
3. Distinction between rational and irrational numbers:
- Rational numbers can be represented as either terminating decimals (such as 0.5 or 1.25) or repeating decimals (such as 0.3333... or 0.6666...), whereas irrational numbers cannot be represented in such forms.
- Rational numbers can also be plotted on the number line since they can be represented as points, while irrational numbers are plotted as non-repeating decimals.
To summarize, rational numbers can be expressed as fractions or ratios of integers, while irrational numbers cannot be written in that form and they have non-repeating and non-terminating decimal representations.