Plotting Real Numbers on a Number Line
Plotting real numbers on a number line is a Grade 11 Algebra 1 skill from enVision Chapter 1 used to compare and order all types of real numbers including fractions, decimals, and irrationals. To compare, convert each number to decimal form. For example, 3/4 = 0.75, sqrt(2) = 1.414, and pi = 3.14159 can be plotted in order from least to greatest. To compare 7/3 and sqrt(5): 7/3 = 2.333 and sqrt(5) = 2.236, so sqrt(5) < 7/3. Irrational numbers require decimal approximations since their decimals are non-terminating and non-repeating.
Key Concepts
Real numbers can be plotted on a number line where each point corresponds to exactly one real number. To compare real numbers, convert them to decimal form and plot their approximate positions: rational numbers have terminating or repeating decimals, while irrational numbers have non terminating, non repeating decimals.
Common Questions
How do you plot irrational numbers on a number line?
Approximate the irrational number as a decimal. For example, sqrt(2) = 1.414..., so plot it just past 1.4 on the number line.
How do you compare 7/3 and sqrt(5)?
Convert both to decimals: 7/3 = 2.333 and sqrt(5) = 2.236. Since 2.236 < 2.333, sqrt(5) < 7/3.
What is the order of -sqrt(3), -1.2, 1/2, sqrt(7) from least to greatest?
Convert: -sqrt(3) = -1.732, -1.2 = -1.2, 1/2 = 0.5, sqrt(7) = 2.646. Order: -sqrt(3) < -1.2 < 1/2 < sqrt(7).
Why do you compare decimals digit by digit from left to right?
Each decimal place represents a smaller unit of value. Comparing from left to right ensures the most significant digits determine the comparison first.
How is comparing negative irrational numbers different from positive ones?
For negative numbers, the one with the larger absolute value is smaller. For example, -1.732 < -1.2 even though 1.732 > 1.2.
What is a rational number versus an irrational number in decimal form?
Rational numbers have terminating or repeating decimals (like 0.75 or 0.333...). Irrational numbers have non-terminating, non-repeating decimals (like sqrt(2) = 1.41421...).