Inequalities with decimals

Learning Objectives Identify and correctly use inequality symbols (<, >, ≤, ≥). Compare any two decimal numbers using appropriate inequality symbols. Order a set of three or more decimal numbers from least to greatest or greatest to least. Solve one-step linear inequalities involving addition or subtraction of decimals. Represent the solution set of a decimal inequality on a number line. Apply inequalities with decimals to solve simple real-world problems. Have you ever needed to compare prices at a store to find the best deal, or check if a measurement is within a certain limit? 🤔 This often involves comparing numbers with decimals! In this lesson, you will learn how to compare and order decimal numbers using special symbols called inequalities. You'll also dis...

TermDefinitionExample InequalityA mathematical statement that compares two expressions using an inequality symbol, showing that one is not necessarily equal to the other.3.5 < 4.2 (3.5 is less than 4.2) DecimalA number that includes a decimal point, representing a fractional part of a whole number. It uses place values like tenths, hundredths, and thousandths.0.75 (seventy-five hundredths), 12.3 (twelve and three tenths) Greater Than (>)An inequality symbol used to show that the number on the left side is larger than the number on the right side.5.8 > 5.1 (5.8 is greater than 5.1) Less Than (<)An inequality symbol used to show that the number on the left side is smaller than the number on the right side.0.25 < 0.3 (0.25 is less than 0.3) Greater Than or Equal To (≥)An inequ...

Rule for Comparing Decimals To compare two decimals, align their decimal points and compare the digits from left to right, starting with the largest place value. If necessary, add trailing zeros to the end of the decimal with fewer digits to make them have the same number of decimal places. This rule helps you accurately determine which decimal is larger or smaller by ensuring you compare digits of the same place value. Addition/Subtraction Property of Inequality If $a < b$, then $a + c < b + c$ and $a - c < b - c$. This also applies to >, ≤, and ≥. You can add or subtract the same decimal number from both sides of an inequality without changing the direction of the inequality symbol. This is useful for isolating a variable. Multiplication/Division Property o...