Todays outcomes are:Todays outcomes are:A1 A1 – model and use power, base and exponents to – model and use power, base and exponents to

reporesent repeated multiplicationreporesent repeated multiplicationA2 A2 – Rename numbers among exponential, standard – Rename numbers among exponential, standard

and expanded formsand expanded forms..

There are many different ways to There are many different ways to show multiplicationshow multiplication

7 x 7 x 7 x77 x 7 x 7 x7(7)(7)(7)(7)(7)(7)(7)(7)7 7 · · 7 7 · · 7 7 · · 77

ExponentsExponents

Exponents are the mathematician’s Exponents are the mathematician’s shorthand for writing multiplication.shorthand for writing multiplication.

7 7 · · 7 7 · · 7 7 · · 7 7 is the same as writing 7is the same as writing 744 since there are four 7’s being since there are four 7’s being multiplied together.multiplied together.

Likewise, (5)(5)(5) is the same as Likewise, (5)(5)(5) is the same as writing 5writing 533 since there are three 5’s since there are three 5’s being multiplied together.being multiplied together.

The format for exponents is:The format for exponents is:

(base)(base)exponentexponent

The exponent tells you how many of the The exponent tells you how many of the base are being multiplied together.base are being multiplied together.

Example:Example:

4433 = 4 = 4 · · 4 4 · · 4 = 644 = 64

More about exponentsMore about exponents

If you are asked to put something into If you are asked to put something into exponential formexponential form then your answer then your answer should have a base and an exponent.should have a base and an exponent. Example: write 5 Example: write 5 · · 5 5 · · 5 in exponential form.5 in exponential form.

Answer: Answer: 5533 If you are asked to put something into If you are asked to put something into

standard formstandard form your answer should show your answer should show no exponents.no exponents. Example: write 6Example: write 64 4 in standard form. in standard form.

Answer: 1296Answer: 1296

Examples: Try theseExamples: Try theseyes that means write them down and answer them!!! yes that means write them down and answer them!!!

1.1. What is the base in each of the following powers? What is the base in each of the following powers? a) 3a) 32 2 b) 1b) 166 c) 7c) 79 9

2.2. What is the exponent in each of these powers.What is the exponent in each of these powers.a) 2a) 24 4 b) 5b) 51818 c) 11c) 110 0

3.3. Write these numbers in exponential form:Write these numbers in exponential form:a) 2 a) 2 · · 2 2 · · 22 b) b) 4 4 · · 44 c) c) 8 8 · · 8 8 · · 8 8 · · 8 8

4.4. Write these numbers in expanded form: Write these numbers in expanded form: a) 3a) 32 2 b) 1b) 166 c) 7c) 79 9

5.5. Evaluate these powers: Evaluate these powers: a) 9a) 92 2 b) 1b) 177 c) 5c) 53 3

6.6. Write each power in exponential form using the indicated base:Write each power in exponential form using the indicated base:a) 16 as a power of 2a) 16 as a power of 2b) 1000 as a power of 10b) 1000 as a power of 10c) 81 as a power of 3c) 81 as a power of 3d) 625 as a power of 5d) 625 as a power of 5

The answers:The answers:1. 1. a) 3a) 3 b) 1b) 1 c) 7c) 72.2. a) a) 4 4 b) b) 1818 c) c) 0 0

3.3. Write these numbers in exponential form:Write these numbers in exponential form:a) 2a) 233 b) b) 4422 c) c) 8844

4.4. Write these numbers in expanded form: Write these numbers in expanded form: a) 3 a) 3 · · 3 3 b) 1 b) 1 · · 1 1 · · 1 1 · · 1 1 · · 1 1 · · 1 1

c) 7 c) 7 · · 7 7 · · 7 7 · · 7 7 · · 7 7 · · 7 7 · · 7 7 · · 7 7 · · 775.5. Evaluate these powers: Evaluate these powers:

a) 81a) 81 b) 1b) 1 c) 125c) 1256.6. Write each power in exponential form using the Write each power in exponential form using the

indicated base:indicated base:a) 2a) 244 b) 10b) 1033 c) 3c) 344 d) 5d) 544

Place Value Review

1 2 3

thousands

4 5 6 . 7 8

hundreds

9

hundred thousands

ten thousands

tens

ones

decimal point

tenths

hundredths

thousandths

Rounding reviewRounding reviewthe steps and rules for rounding the steps and rules for rounding

numbersnumbers Step 1: identify the number in the place Step 1: identify the number in the place

you are being asked to round to.you are being asked to round to. Step 2: Look at the number to the right of Step 2: Look at the number to the right of

that numberthat number• Rule 1: if the number to the right is a 5 or larger Rule 1: if the number to the right is a 5 or larger

then increase your original number by 1then increase your original number by 1• Rule 2: if the number to the right is a 4 or lower Rule 2: if the number to the right is a 4 or lower

then the original number stays the samethen the original number stays the same

Step 3: change all the digits to the right Step 3: change all the digits to the right into zeros.into zeros.

Examples: Try theseExamples: Try theseyes that means write them down and answer them!!! yes that means write them down and answer them!!!

1.1. In the number 1 876 345.920 which digit is in In the number 1 876 345.920 which digit is in the following place?the following place?a) ones ___a) ones ___ b)hundredths ____b)hundredths ____c) millions ___c) millions ___ d)thousands ____d)thousands ____

2.2. In the number 472 985.136 what is the place In the number 472 985.136 what is the place value of:value of:a) 8 __________a) 8 __________ b) 4 ___________b) 4 ___________c) 1 __________c) 1 __________ d) 9 ___________d) 9 ___________

3.3. Round 349 251 to the:Round 349 251 to the:a) tens place ___________a) tens place ___________b) thousands place __________b) thousands place __________c) hundreds place ___________c) hundreds place ___________

AnswersAnswers

1.1. a) 5a) 5 b)2b)2 c) 1c) 1 d)6d)6

2.2. a) tensa) tensb) hundred thousandsb) hundred thousandsc) tenths c) tenths d) hundredsd) hundreds

3.3. a) 349 250a) 349 250b) 349 000b) 349 000c) 349 300c) 349 300

Expanded Notation of Whole Expanded Notation of Whole NumbersNumbers

Expanded notation is a way of writing a number Expanded notation is a way of writing a number as the some of the values of its’ digits.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 #2Example #2• Standard form: 52 908Standard form: 52 908• Expanded form: Expanded form:

(5 x 10 000) + (2 x 1000) + (9 x 100) + (0 x 10) + (8 x 1) (5 x 10 000) + (2 x 1000) + (9 x 100) + (0 x 10) + (8 x 1)