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# The real number system

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### The real number system

1. 1. The Real Number System<br />
2. 2. N : 1,2,3,….<br />Z : …,-2,-1,0,1,2,..<br />Q :<br />Irational:<br />
3. 3. Real Numbers<br />Rational Numbers<br /> ¼ ⅓<br />0.6 <br />- ⅔ √0.25<br />Irrational<br />Numbers<br />π<br />0.101001<br />√2<br />Integers<br />- 4 -3<br />-8<br />Whole Numbers<br />0<br />Natural<br />Numbers<br />2 <br />5<br />
4. 4. Concept Summary<br />
5. 5. Operation of Integers<br />
6. 6. Four Fundamental Operations<br />
7. 7.
8. 8. 1.1<br />Integers and Their Symbols<br />A<br />+5<br />0<br />-5<br />+5<br />-5<br />0<br />Positive and Negative Numbers<br />The numbers 5 and -5 can be drawn on a vertical or a horizontal line as follows. <br /> thermometer<br />Horizontal number line<br />You may write:<br /><ul><li> the temperature of 5 degrees above zero as 5 ºC,
9. 9. the temperature of 5 degrees below zero as -5 ºC. </li></ul>Verticalnumber line<br />
10. 10. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6<br />Positive integers<br />Negative integers <br />0 is neither positive nor negative <br />A set of integers; ..., 3, 2, 1, 0, 1, 2, 3, ... , can be symbolized as Z. <br /><ul><li>The complete number line of integers can be drawn as follows.</li></ul>Natural numbers ( bilanganAsli ) : 1, 2, 3, 4, …Whole numbers ( bilanganCacah ) : 0, 1, 2, 3, 4, …Integers ( bilanganBulat ) : …, -2, -1, 0, 1, 2, …<br />
11. 11. a. Determine all integers between 5 and 4.<br />Example 1<br />Solution:<br /> 4, 3, 2, 1, 0, 1, 2, 3<br />b. Write all even integers between 6 and 11.<br />Solution:<br /> The even integers between 6 and 11 are 4, 2, 0, 2, 4, 6, 8, and 10<br />c. Write all odd integers between 7 and 8.<br />Solution:<br /> The odd integers between 7 and 8 are -5, -3, -1, 1 , 3 , 5, and 7<br />
12. 12. B<br />-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6<br />Comparing and Ordering Integers<br />-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6<br />increase<br /> decrease<br />What if we use a vertical number line?<br />Change the sign  to <, >, or = on 4 7<br /> Solution:<br />Example 2<br />The number 4 is located on the right side of 7. Therefore, 4 > 7.<br />
13. 13. Problem 1<br />Arrange the following numbers from the least to the greatest.<br />a. 5, 3, 6, 6, 2, 4, 1<br />b. 9, 5, 6, 12, 17, 8, 14 <br />Problem 1<br />Solution :<br />a. -6, -3, -1, 2, 4, 5, 6<br />b. -14, -12, -5, 6, 8, 9, 17 <br />
14. 14. In a mathematics test, the score for the right answer is 4, for the wrong answer is -1, and 0 for failing to answer.<br />Complete the table below (use a spreadsheet, if possible) and then sort the students based on their scores from the highest to the lowest.<br />Problem 2<br />17<br />20<br />18<br />30<br />31<br />32<br />27<br />25<br />