* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Compare & Order Rational Numbers
Survey
Document related concepts
Foundations of mathematics wikipedia , lookup
Georg Cantor's first set theory article wikipedia , lookup
Infinitesimal wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
History of logarithms wikipedia , lookup
Large numbers wikipedia , lookup
Location arithmetic wikipedia , lookup
Real number wikipedia , lookup
Approximations of π wikipedia , lookup
P-adic number wikipedia , lookup
Transcript
Take out homework and have it ready to be checked!!! DO NOW Objective: Compare and order Rational numbers Vocabulary: Rational Numbers Irrational Number • Common Denominator Least Common Denominator • • • What is a rational number??? Rational Number: any number that can be expressed as a fraction Ex. Fractions, decimals, %’s, and integers (whole #’s that are + and -) Examples of Rational Numbers 20% -5 Rational Numbers Integers -35 -27 Whole Numbers 1 0.8 -3 5 2.22 -1.444… 35 3 6 1 2 1.3 Irrational Number: a number that does not terminate AND does not repeat Pi (π) is an irrational number… 3.1415926535897932384626433832795028841971693993751 05820974944592307816406286208998628034825342117067 98214808651328230664709384460955058223172535940812 84811174502841027019385211055596446229489549303819 64428810975665933446128475648233786783165271201909 14564856692346034861045432664821339360726024914127 37245870066063155881748815209209628292540917153643 67892590360011330530548820466521384146951941511609 43305727036575959195309218611738193261179310511854 80744623799627495673518857527248912279381830119491 Common Denominator: A common number that both denominators fit into Examples Comparing Rational Numbers Which is greater, or ? 7 9 2 9 When two fractions have the same denominator, just compare the numerators. 7 2 > because 7 > 2. 9 9 Least Common Denominator (LCD): the smallest number that both denominators will fit into. Examples Which is greater, or ? 3 4 4 5 When two fractions have different denominators, find the LCD, then compare. Which is greater, 34 or 45 ? What’s the LCD of both fractions? The LCD of the denominators 4 and 5 is 20. Answer: Compare the Following Fractions 1 4 2 7 1 7 4 28 2 8 7 28 1 4 5 12 1 3 5 5 12 12 1 4 3 12 5 12 2 6 3 4 2 4 6 12 3 9 4 12 2 6 < 2 7 > 1 3 < 3 4 Comparing and Ordering 2-11 Rational Numbers Additional Example 1A: Comparing Fractions Compare the fractions. Write < or >. 7 5 9 8 The LCM of the denominators 9 and 8 is 72. 7 = 9 5 = 8 56 > 72 Course 2 7 · 8 = 56 9·8 72 5 · 9 = 45 8·9 72 45 , and so 72 7 .> 5 9 8 Write equivalent fractions with 72 as the denominator. Compare the numbers. Ordering Rational Numbers To put decimals in order, line up the decimal points and compare using place value. Ordering Rational Numbers Compare the decimals 0.427 > 0.425 0.427 0.425 Compare the numbers that are different… 7 > 5 so… Comparing and Ordering 2-11 Rational Numbers Additional Example 3: Ordering Fractions and Decimals Order 4 , 0.93, and 0.9 from least to greatest. 5 Write as decimals with the same number of places. 4 = 0.80 0.93 = 0.93 0.9 = 0.90 5 Graph the numbers on a number line. 0.93 0 0.2 0.4 0.80 < 0.90 < 0.93 0.6 0.8 1 Compare the decimals in order. From least to greatest, the numbers are 0.9, 0.93, 4 . 5 Course 2 Comparing and Ordering 2-11 Rational Insert Lesson Title Here Numbers Lesson Practice Compare the fractions. Write > or <. 3 or 4 > 2. 5 or 2 8 3 10 7 Compare the decimals. Write < or >. 1. 3. 0.32 and 0.312 < > 5 , 0.8, 0.826 from least to greatest. 6 5 0.8, 0.826, 6 4. Order Course 2 Converting Fractions to Decimals • To convert a Fraction to a Decimal manually, follow these steps: • Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s. • Step 2: Multiply both top and bottom by that number. • Step 3. Then write down just the top number, putting the decimal place in the correct spot (one space from the right for every zero in the bottom number) Method #1: Converting with Proportions • Example # 1: Express 3/4 as a Decimal • Step 1: We can multiply 4 by 25 to become 100 • Step 2: Multiply top and bottom by 25 3 4 = 75 100 Example # 1 continued…. • Step 3: Write down 75 with the decimal place 2 spaces from the right (because 100 has 2 zeros); • Answer = 0.75 • Can you explain what we just did? • Try to express ¼ as a decimal using method # 1. Try to express ¼ as a decimal using method # 1. Method #2: Convert by Dividing Example #1: to write 5/8 as a decimal, we need to calculate 5 ÷ 8: 0.625 8 √ 5.000 So = 0.625 as a decimal. Try this example: write 4/5 as a decimal using division (method #2). write 4/5 as a decimal using division (method #2) Write 3/8 as a decimal using division (method 2) Write 2/7 as a decimal using division (method 2) Convert decimals to Percents • To convert a decimal to a percent Step 1:Multiply the decimal by 100. Step 2: Move the decimal to the right two places. 0.45 Convert decimals to Percents 1. 2. 3. 4. 5. 0.38 0.235 0.005 1.05 0.023