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

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

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.

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

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

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) What is the exponent in each of these powers. a) 2 4 b) 5 18 c) 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) Evaluate these powers: a) 9 2 b) 1 7 c) 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

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) 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) Write each power in exponential form using the indicated base: a) 2 4 b) 10 3 c) 3 4 d) 5 4

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

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.

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 which digit is in the following place? a) ones ___b)hundredths ____ c) millions ___d)thousands ____ 2. In the number what is the place value of: a) 8 __________b) 4 ___________ c) 1 __________d) 9 ___________ 3. Round to the: a) tens place ___________ b) thousands place __________ c) hundreds place ___________

Answers 1. a) 5b)2c) 1d)6 2. a) tens b) hundred thousands c) tenths d) hundreds 3. a) b) c)

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: Standard form: Expanded form: (5 x ) + (2 x 1000) + (9 x 100) + (0 x 10) + (8 x 1)Expanded form: (5 x ) + (2 x 1000) + (9 x 100) + (0 x 10) + (8 x 1)