Decimal number lines

Learning Objectives Calculate unknown side lengths of right triangles using the Pythagorean Theorem. Identify when the Pythagorean Theorem yields an irrational number. Approximate irrational square roots to a specified decimal place. Construct and label a decimal number line with appropriate intervals. Accurately locate and plot approximated irrational numbers on a decimal number line. Compare and order irrational numbers by approximating their decimal values and placing them on a number line. Ever wondered how we can precisely locate a number like the square root of 2 on a number line? 🤔 It's not as simple as finding an integer, but with decimal number lines and the Pythagorean Theorem, we can pinpoint these mysterious values! In this lesson, you'll learn how th...

TermDefinitionExample Decimal Number LineA number line where the space between integers is divided into smaller units (tenths, hundredths, etc.) to represent decimal numbers.A number line segment from 2 to 3, marked with 2.1, 2.2, 2.3, ..., 2.9. Pythagorean TheoremA fundamental theorem in geometry that states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs).If a right triangle has legs of length 3 and 4, the hypotenuse is $\sqrt{3^2 + 4^2} = \sqrt{9+16} = \sqrt{25} = 5$. Irrational NumberA real number that cannot be expressed as a simple fraction (a ratio of two integers). Its decimal representation is non-terminating and non-repeating.$\sqrt{2}$, $\sqrt{5}$, $\pi$ are irratio...

Pythagorean Theorem $a^2 + b^2 = c^2$ Used to find the length of an unknown side in a right-angled triangle, where 'a' and 'b' are the lengths of the legs, and 'c' is the length of the hypotenuse. Approximating Irrational Square Roots To approximate $\sqrt{x}$ to a decimal place, find two consecutive perfect squares that $x$ lies between. Then, test decimal values between their square roots by squaring them until you reach the desired precision. This rule helps us estimate the decimal value of irrational numbers (like $\sqrt{7}$) so they can be placed on a decimal number line. For example, since $2^2=4$ and $3^2=9$, $\sqrt{7}$ is between 2 and 3. Testing $2.6^2 = 6.76$ and $2.7^2 = 7.29$ tells us $\sqrt{7}$ is between 2.6 and 2.7.