Start-up #20 Oct 12th Suppose we start with a single bacterium, which divides every hour (binary fission). After one hour we have 2 bacteria, after two hours we have 4 bacteria, after three hours 8 bacteria, and so on. a) Create a diagram of the bacterial growth per generation. b) Write an exponential expression to represent how many bacteria are present in each generation. c) Use your expression to find the number of bacterium that are present in the 12th generation. Extension: E. coli bacteria can divide every 20 minutes and a new population starts with just a single bacterium, how many bacterium will be present in 8 hours?

Unit 3 Rational Numbers

3.1 – What is a rational number? Chapter 3 FOCUS: Compare and order rational numbers. KEY WORDS Rational number Irrational number

evaluate It doesn’t matter if the negative sign is on the numerator, or on the denominator—the fraction is still negative. They are equivalent. The same way that positive integers all have negative counterparts (or opposites), each fraction has a negative opposite as well.

Rational numbers A rational number is any number that can be written in the form of a/b where a and b are integers, and b ≠ 0. In other words, the set of rational numbers includes all integers, fractions and terminating or repeating decimals. Rational Numbers Non-Rational Numbers A fraction can be written as a . or decimal. Any mixed number can be written as an improper fraction. So, . are rational numbers. Any can be written as a fraction with denominator 1. A fraction can be written as a terminating or repeating decimal. Any mixed number can be written as an improper fraction. So, mixed numbers are rational numbers. Any integer can be written as a fraction with denominator 1.

Always label the number line using the original values! 102/2015 EXAMPLE 2 Write the rational number represented by each letter on the number line, as a decimal and as a fraction. -7 9/10 = -7.9 -7 2/10 = -7.2 EXAMPLE 3 Show each set of numbers on a number line. Order the numbers from least to greatest.  1.5, -11/2, -2.5, ½ 1.5, -5.5, -2.5, 0.5 Hint: Write each number as a decimal. Use a calculator when necessary. Always label the number line using the original values!

example Find three rational numbers between each pair of numbers. a) –0.25 and –0.26 b) –1/2 and –1/4 a) Remember, we can always add a zero to the end of a decimal, without changing the value. So, –0.25 and –0.26 can also be written as –0.250 and –0.260. What numbers are between 250 and 260? 251, 252, 253, etc… So possible answers are –0.251, –0.252, –0.253. b) Try it! What are some different ways that we could solve this?

example Order these rational numbers from least to greatest: 1.13, –10/3, –3.4, 2.777… , 3/7, –2 2/5 Putting all of the numbers into decimal form may be the easiest way to do these types of questions. –10/3 = –3.333… 3/7 = 0.429 –2 2/5 = –2.4 Remember, negatives are smaller than positives: –3.4, –3.333…, –2.4, 0.429, 2.777… Now, put the original numbers back in:  –3.4, –10/3, –2 2/5, 3/7, 2.777…

Pg. 101-103 # 8, 9, 10, 16, 21, 22, 24 Independent practice