1.10 Compare Real Numbers rational irrational.pptx

1.10 Compare Real Numbers rational irrational.pptx

1. Page 89 Lesson 1-10 Compare Real Numbers

2. What’s Rational Number? What’s Irrational Number? A  rational number  is any number that can be made by dividing two  integers . All rational numbers can be written in the form where  p  and  q  are integers and  q  is not zero.  

3. Numbers that are not rational are called irrational numbers. The square root of non perfect square are irrational numbers . The set of rational and irrational numbers together make up the set of Real Numbers i.e.,  

4. = 1.414213562… 1.21231234… = 3.14159265359…

5. Take Note of these Rational Numbers:  is a rational number. –5 is a rational number because it can be written as  - 4.75  is a rational number because it can be written as   –0.36 is a rational number because it can be written as   1.  is a rational number because it can be written as  is a rational number because it can be written as   A decimal rational number can be in form as a repeating or terminating decimal.

6. 1 . 0.2525... 2. 3.   The decimal is a repeating decimal, therefore, it is a rational number because it also be written as   Since the = 6. 6 is a natural number and an integer, therefore, it is a rational number.   The = -2.645751311... The decimal does not repeat nor terminate; therefore, it is an irrational number.  

7. a. The = 3.16227766. Since the decimal does not repeat nor terminate, it is an irrational number.   b. The can be written as -2.4; since -2.4 is a terminating decimal, it is a rational number.   c. Since the = 10; 10 is a natural number and a whole number, it is a rational number.  

8. Solution: Step 1: write each number as a decimal. = 2.645751311… = 2.6666666666…   Step 2: Compare the decimals. 2.64 5751311… is less than 2.66 66666… <   No. 5 Step 1: 15.7% = 0.157 = 0.141 Step 2: 0.157 is greater than 0.141   15.7% >  

9. Solution: Step 1: write each number as a decimal. = 5.48 6 = 6.00 = 5.80 5.3 = 5.37   Step 2: Compare the decimals. 5.37 < 5.48 < 5.80 < 6.00 So, from least to greatest order is 5.3 , , , and 6  

10. d. < e. > 4.03 f. = 250%   g < < <  

11. Homework Assignment (page 92):