## An Elementary Treatise on Diff. Eqns. and Their Applns. by H. Piaggio

By H. Piaggio

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Geometrically, this means that a lies to the left of b on the number line. 5 œ∑2 _3 E X AM P L E 1 2Յ2 _2 | _1 0 1 2 3 4 5 6 7 8 Graphing Inequalities (a) On the real line, graph all the numbers x that satisfy the inequality x Ͻ 3. (b) On the real line, graph all the numbers x that satisfy the inequality x Ն Ϫ2. ▼ SO LUTI O N 0 (a) We must graph the real numbers that are smaller than 3—those that lie to the left of 3 on the real line. The graph is shown in Figure 3. Note that the number 3 is indicated with an open dot on the real line, since it does not satisfy the inequality.

692 ϫ 104 123 4 places ✎ Ǡ 5 places ▲ Practice what you’ve learned: Do Exercises 73 and 75. E X AM P L E 7 | Changing from Decimal to Scientific Notation Write each number in decimal notation. 0000046271 1424 3 Move decimal 6 places to the left 6 places To use scientific notation on a calculator, use a key labeled EE or EXP or EEX to enter the exponent. 629 2ND EE ✎ ▲ Practice what you’ve learned: Do Exercises 81 and 83. Scientific notation is often used on a calculator to display a very large or very small number.

We start with the natural numbers: 1, 2, 3, 4, . . The different types of real numbers were invented to meet specific needs. For example, natural numbers are needed for counting, negative numbers for describing debt or below-zero temperatures, rational numbers for concepts such as “half a gallon of milk,” and irrational numbers for measuring certain distances, such as the diagonal of a square. The integers consist of the natural numbers together with their negatives and 0: . . , Ϫ3, Ϫ2, Ϫ1, 0, 1, 2, 3, 4, .