Ordering Real Numbers on a Number Line
Ordering Real Numbers on a Number Line is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 7: Real Numbers and the Pythagorean Theorem. Students learn to compare and order mixed sets of rational and irrational numbers by approximating irrational values as decimals, then plotting all numbers on a number line to determine their relative order from least to greatest.
Key Concepts
Property To order a mixed set of rational and irrational numbers visually, approximate the irrational numbers as decimals and convert any fractions. Then, plot all numbers on a number line to determine their relative positions. Numbers always increase in value from left to right on the number line.
Examples Order from least to greatest: 2.5, $\sqrt{7}$, $\frac{8}{3}$ Since $\sqrt{7} \approx 2.646$ and $\frac{8}{3} \approx 2.667$, the relative order is $2.5 < \sqrt{7} < \frac{8}{3}$. Order from least to greatest: $\sqrt{15}$, 4, 3.9, $\sqrt{14}$ Since $\sqrt{15} \approx 3.873$ and $\sqrt{14} \approx 3.742$, the sequence is $\sqrt{14} < \sqrt{15} < 3.9 < 4$.
Common Questions
How do you order a mix of rational and irrational numbers?
Approximate any irrational numbers (like square roots) as decimals and convert fractions to decimals. Then compare the decimal values to determine the order from least to greatest.
How do you order 2.5, the square root of 7, and 8/3 from least to greatest?
Approximate: square root of 7 is about 2.646 and 8/3 is about 2.667. So the order is 2.5 < sqrt(7) < 8/3.
Which direction is greater on a number line?
Numbers increase in value from left to right on a number line. A number to the right of another is always greater.
How do you compare square root of 14 and square root of 15?
Since 14 < 15, sqrt(14) < sqrt(15). Approximately sqrt(14) is 3.742 and sqrt(15) is 3.873.