MJ2A

1. MJ2A Ch 5.2 – Rational Numbers

2. Bellwork 1. Describe in words how to convert a fraction into a decimal.

3. Assignment Review • Text p. 203 # 13 – 43

4. Objective • Students will write rational numbers as fractions and identify and classify rational numbers.

5. Review • Yesterday we discussed converting fractions into decimals. • To convert a fraction into a decimal simply divide the numerator by the denominator • Example ¾ = 3 divided by 4 = 0.75 • Example 5/8 = 5 divided by 8 = 0.625

6. Before we begin… • Working with fractions and decimals will become a part of your everyday adult life… • Raise your hand if you can name jobs that people do where they have to know how to work with fractions and decimals… • Today we will explore more with Fractions and decimals in the form of: • Rounding decimals • Writing rational numbers as fractions • Classifying rational numbers

7. Rounding Decimals

8. Rounding Decimals • The rules for rounding decimals are: • Determine the position to round to. • Look at the number to the right of the position you are rounding to. • If the number is 5 or greater, then change the number in the position your are rounding to the next number up. Then drop all the numbers after that position. • If the number is 4 or less, leave the position you are rounding alone and drop all the following numbers.

9. Rounding Example Round 8.37258 to the hundredths 1. This is the hundredths position 2. Look at the number to the right of the hundredths position 3. Since the number after the hundredths position is less than 4 leave the 7 alone and drop the rest of the numbers Your rounded number is 8.37

10. Rounding Example Round 12.36124 to the tenths 1. This is the tenths position 2. Look at the number to the right of the tenths position 3. Since the number after the tenths position is greater than 5 change the 3 to a 4 and drop the rest of the numbers Your rounded number is 12.4

11. Your Turn • Round to the 10ths 8.75432 • Round to the 100ths 6.42183 • Round to the 1000ths 0.86590

12. Converting Decimals to Fractions • Terminating Decimals • Repeating Decimals

13. Types of Decimals • When working with decimals there are two types that you need to be aware of • Terminating Decimals • Repeating Decimals • When converting decimals to fractions the process is different for each type of decimal

14. Converting a Terminating Decimal to a Fraction • What is a terminating decimal? • To convert a terminating decimal to a fraction simply determine what place value the decimal is and place it over the place value number • Example: .45 is in the 100ths place value. To write it as a fraction drop the decimal and place 45 over 100 or 45 100 Note: As a rule of thumb… all fractions are expressed in simplest form unless otherwise requested

15. Your Turn • In the notes section of your notebook write the following decimals as fractions in simplest form • .4 • -0.35 • 7.32

16. Converting a Repeating Decimal to a Fraction • To convert a repeating decimal to a fraction determine the place value, then convert the place value to 9’s then place the number over the 9’s.

17. Example: Converting a Repeating Decimal to a Fraction 0.72 1. The repeating decimal is in the 100ths place value. 2. Convert the 100ths place value to 99 3. Drop the decimal point and place the 72 over 99 The decimal can be converted to the fraction 72 99

18. Repeating Decimal Proof • I suppose that you are wondering where the 9 comes from…We can prove algebraically that when you have a repeating decimal you use 9’s in the denominator of your answer • Supposed I wanted to convert 0.5 to a decimal ….I could use the following logic…

19. Repeating Decimal Proof • To set up this proof, you have to make an assumption • The first step is to let N= 0.5 or 0.555… • The second step is to get rid of the decimals. Therefore, I can multiply 0.555… times 10 to get 5.555…, Therefore, 10N = 5.555… • Now I can get rid of the repeating decimal by subtracting 10n – n…It looks like this…

20. Repeating Decimal Proof 10N = 5.555… – N = 0.555… 9N = 5 9 9 N = 5 9

21. Observation • In the notes section of your notebook convert the following repeating decimals to fractions • 0.2 • 0.35 • 0.625 • 0.7123 • Identify the pattern…

22. Your Turn • In the notes section of your notebook express the following as a fraction in simplest form… • 0.9 • 2.35 • .8

23. Classifying Rational Numbers • A rational number is any number that can be expressed as the quotient a b of two integers a and b, where b≠ 0. • We have previously discussed the real number system as being comprised of rational and irrational numbers… • We can classify rational numbers in the following manner…

24. Rational Numbers ¾ Integers {…-3, -2, -1, 0, 1, 2, 3…} 0.7 4 ½ Whole Numbers {0, 1, 2, 3…} Natural Numbers {1,2,3…} -3.2222 2/3 1.8

25. Classifying Rational Numbers • To classify a rational number: • Determine what group it belongs to… • Then place it in the diagram and it belongs to that group and every larger group….

26. Summary • In the notes section of your notebook summarize the key concepts covered in today’s lesson • What are the rules for rounding decimals? • How do you convert a terminating decimal to a fraction? • How do you convert a repeating decimal to a fraction? • How do you classify a rational number?

27. Assignment • Text p. 208 # 12 – 27 Reminder: • This assignment is due tomorrow • I do not accept late assignments • I do not accept assignments with answers only!