1. Using Exponents to Write Large Numbers June 25, 2012

2. For Learning to Happen! Clear your desk of anything that may distract you. Remove all other thoughts from your mind. Pay close attention. Try all the examples. Ignore all other distractions.

3. Objectives Write numerals in exponential form Write numerals in exponential form Express in standard form the numerals in exponential form or expanded exponential form or vice versa Express in standard form the numerals in exponential form or expanded exponential form or vice versa

4. Exponents of Ten What Is the Standard Form of These Tens? 2 10 3 4 5 100 1,000 10,000 100,000

5. Exponents of Ten Notice that the number of zeros matches the exponent number 2 10 3 4 5 100 1,000 10,000 100,000

6. Multiplying Multiples of Ten Multiply These Numbers 100 x 2 = 1,000 x 3 = 10,000 x 7 = 100,000 x 9 = 200 3,000 70,000 900,000

7. Multiplying Multiples of Ten Did you notice that all you have to do is multiply 1 x whole number & add the zeros behind? 100 x 2 = 1,000 x 3 = 10,000 x 7 = 100,000 x 9 = 200 3,000 70,000 900,000

8. Short Cut for Writing Large Numbers Combine these two steps for writing large numbers. 6 x 10 2 = 6 x (10 x 10) = 6 x 100 = 600 600

9. Short Cut for Writing Large NumbersRemember! The exponent is the same as the number of zeros. 6 x 10 2 = 600

10. What is the Standard Number? 7 x 10 2 = 700

11. What is the Standard Number? 8 x 10 3 = 8,000

12. What is the Standard Number? 9 x 10 4 = 90,000

13. What is the Standard Number? 4 x 10 2 = 400

14. What is the Standard Number? 13 x 10 2 = 1 300

15. What is the Standard Number? 216 x 10 1 = 2 160

16. What is the Exponent Form? 5 x 10 2 = 500

17. What is the Exponent Form? 6 x 10 3 = 6,000

18. What is the Exponent Form? 9 x 10 4 = 90,000

19. What is the Exponent Form? 7 x 10 5 = 700,000

20. What is the Exponent Form? 65 x 10 4 = 650,000

21. What is the Exponent Form? 107 x 10 3 = 107,000

22. The human eye blinks about once every five seconds. In 16 waking hours, an average person blinks about 11 500 times a day or 4 200 000 times a year. Study how each numeral is written in Expanded exponential form in 3 ways.

23. 1. Giving the value of each digit 2. Multiply each digit by its place value 3. Multiply each digit by powers of 10 11 500 Study how each numeral is written in Expanded exponential form in 3 ways. 10 000 + 5001 000 + + 1 x 10 000 ++ 1 x 1 0005 x 100 (1 x 10 4 ) (1 x 10 3 )(5 x 10 2 ) +

24. 1. Giving the value of each digit 2. Multiply each digit by its place value 3. Multiply each digit by powers of 10 Expanded Exponential Form of 23 400 23 400 20 000 + 4003 000 + + 2 x 10 000 ++ 3 x 1 0004 x 100 (2 x 10 4 ) (3 x 10 3 ) (4 x 10 2 ) + (2 x 10 4 ) + (3 x 10 3 ) + (4 x 10 2 ) Exponential Form of 23 400? 234 x 10 2

25. 1. Giving the value of each digit 2. Multiply each digit by its place value 3. Multiply each digit by powers of 10 Expanded Exponential Form of 6 052 6 052 6 000 + 250 + + 6 x 1 000 ++ 5 x 102 x 1 (6 x 10 3 ) (5 x 10 1 ) (2 x 10 0 ) + (6 x 10 3 ) + (5 x 10 1 ) + (2 x 10 0 )