1. Todays outcomes are: A1 – model and use power, base and exponents to reporesent repeated multiplication A2 – Rename numbers among exponential, standard and expanded forms.

2. There are many different ways to show multiplication  7 x 7 x 7 x7  (7)(7)(7)(7)  7 · 7 · 7 · 7

3. Exponents  Exponents are the mathematician’s shorthand for writing multiplication.  7 · 7 · 7 · 7 is the same as writing 7 4 since there are four 7’s being multiplied together.  Likewise, (5)(5)(5) is the same as writing 5 3 since there are three 5’s being multiplied together.

4. The format for exponents is: (base) exponent The exponent tells you how many of the base are being multiplied together. Example: 4 3 = 4 · 4 · 4 = 64

5. More about exponents  If you are asked to put something into exponential form then your answer should have a base and an exponent. Example: write 5 · 5 · 5 in exponential form. Answer: 5 3 Example: write 5 · 5 · 5 in exponential form. Answer: 5 3  If you are asked to put something into standard form your answer should show no exponents. Example: write 6 4 in standard form. Answer: 1296 Example: write 6 4 in standard form. Answer: 1296

6. Examples: Try these yes that means write them down and answer them!!! Examples: Try these yes that means write them down and answer them!!! 1. What is the base in each of the following powers? a) 3 2 b) 1 6 c) 7 9 2. What is the exponent in each of these powers. a) 2 4 b) 5 18 c) 11 0 3. Write these numbers in exponential form: a) 2 · 2 · 2b) 4 · 4c) 8 · 8 · 8 · 8 4. Write these numbers in expanded form: a) 3 2 b) 1 6 c) 7 9 5. Evaluate these powers: a) 9 2 b) 1 7 c) 5 3 6. Write each power in exponential form using the indicated base: a) 16 as a power of 2 b) 1000 as a power of 10 c) 81 as a power of 3 d) 625 as a power of 5

7. The answers: 1. a) 3 b) 1 c) 7 2. a) 4 b) 18 c) 0 3. Write these numbers in exponential form: a) 2 3 b) 4 2 c) 8 4 4. Write these numbers in expanded form: a) 3 · 3 b) 1 · 1 · 1 · 1 · 1 · 1 c) 7 · 7 · 7 · 7 · 7 · 7 · 7 · 7 · 7 5. Evaluate these powers: a) 81 b) 1 c) 125 6. Write each power in exponential form using the indicated base: a) 2 4 b) 10 3 c) 3 4 d) 5 4

8. Place Value Review 1 hundred thousands 2 ten thousands 3 thousands 4 hundreds 5 tens 6 ones. decimal point 7 tenths 8 hundredths 9 thousandths

9. Rounding review the steps and rules for rounding numbers  Step 1: identify the number in the place you are being asked to round to.  Step 2: Look at the number to the right of that number Rule 1: if the number to the right is a 5 or larger then increase your original number by 1Rule 1: if the number to the right is a 5 or larger then increase your original number by 1 Rule 2: if the number to the right is a 4 or lower then the original number stays the sameRule 2: if the number to the right is a 4 or lower then the original number stays the same  Step 3: change all the digits to the right into zeros.

10. Examples: Try these yes that means write them down and answer them!!! Examples: Try these yes that means write them down and answer them!!! 1. In the number 1 876 345.920 which digit is in the following place? a) ones ___b)hundredths ____ c) millions ___d)thousands ____ 2. In the number 472 985.136 what is the place value of: a) 8 __________b) 4 ___________ c) 1 __________d) 9 ___________ 3. Round 349 251 to the: a) tens place ___________ b) thousands place __________ c) hundreds place ___________

11. Answers 1. a) 5b)2c) 1d)6 2. a) tens b) hundred thousands c) tenths d) hundreds 3. a) 349 250 b) 349 000 c) 349 300

12. Expanded Notation of Whole Numbers  Expanded notation is a way of writing a number as the some of the values of its’ digits. Example #1: Example #1: Standard form: 372Standard form: 372 Expanded Form: (3 x 100) + (7 x 10) + (2 x 1)Expanded Form: (3 x 100) + (7 x 10) + (2 x 1) Example #2 Example #2 Standard form: 52 908Standard form: 52 908 Expanded form: (5 x 10 000) + (2 x 1000) + (9 x 100) + (0 x 10) + (8 x 1)Expanded form: (5 x 10 000) + (2 x 1000) + (9 x 100) + (0 x 10) + (8 x 1)