1. CONFIDENTIAL 1 Grade 8 Exponents/Scientific Notation

2. Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. Scientific Notation is based on powers of the base number 10. The second number is called the base. It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 10 11 the number 11 is referred to as the exponent or power of ten. Scientific notation The number 123,000,000,000 in scientific notation is written as : 1.23 ×10 11 The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10.

3. Exponents The "exponent" stands for however many times the thing is being multiplied. The thing that's being multiplied is called the "base". This process of using exponents is called "raising to a power", where the exponent is the "power". "5 3 " is "five, raised to the third power". Example 1: 2 x 2 x 2 x 2 x 2 = 2 5 i.e., 2 raised to the fifth power Exponential notation is an easier way to write a number as a product of many factors.

4. Whole numbers can be expressed in standard form, in factor form and in exponential form. Exponential notation makes it easier to write a number as a factor repeatedly. A number written in exponential form is a base raised to an exponent. The exponent tells us how many times the base is used as a factor. Write 10 3, 3 6, and 1 8 in factor form and in standard form. Exponential Form Factor Form Standard Form 10 3 10 × 10 × 101,000 3636 3 ×3 ×3 × 3 × 3 ×3729 1818 1 ×1 × 1 ×1 × 1 × 1 × 1 × 11

5. If a negative number is raised to an even power, the result will be positive. (-2) 4 = - 2 × - 2 × - 2 × - 2 = 16 If a negative number is raised to an odd power, the result will be negative. (-2) 5 = - 2 × - 2 × - 2 × - 2 × - 2 = -32 The negative number must be enclosed by parentheses to have the exponent apply to the negative term. Note that (-2) 4 = - 2 × - 2 × - 2 × - 2 = 16 and -2 4 = -(2 × 2 × 2 × 2) = -16

6. Write in scientific notation: 35,800 Place the decimal point between the first two non-zero numbers, 3 and 5. Since the 3 was in the ten-thousands place, the power of 10 is 10 4. The number in the scientific notation is 3.58 × 10 4. To change the number from scientific notation into standard notation, you can also count the number of times the decimal point moved to determine the power of 10. 35,800 = 3 5 8 0 0 = 3.58 × 10 4 Decimal point moves 4 places to the left.

7. To change the number from scientific notation into standard notation, begin with place value indicated by the power of 10. Add zeroes as place holders when necessary. 0.0079 = 0. 0 0 7 9 = 7.9 × 10 -3 Write in scientific notation: 0.0079 Decimal point moves 3 places to the right.

8. Let us do some practice problems!

9. CONFIDENTIAL 9 1) What is the number 0.000512 denoted as in the scientific notation? a)51.2 × 10 4 b)51.2 × 10 -4 c)5.12 × 10 4 d)5.12 × 10- 4

10. CONFIDENTIAL 10 2) What is the number 1.512 × 10 6 denoted as in the standard notation? a)1512000000 b)1512000 c)151200000 d)15120000 b) 1512000

11. CONFIDENTIAL 11 3) Pluto’s mean distance from Sun is 3,670,000.000 miles. What is this number in the scientific notation? a)3.67 × 10 9 miles b)3.67 × 10 8 miles c)3.67 × 10 7 miles d)3.67 × 10 11 miles a) 3.67 × 10 9 miles

12. CONFIDENTIAL 12 4) To write 3.18 ×10 7 in standard notation, how many times will the decimal point move? a)7 places to the right. b)5 places to the right. c)7 places to the left. d)5 places to the right. a) 7 places to the right.

13. CONFIDENTIAL 13 5) Which number is the largest? a)3.67 × 10 -9 b)3.67 × 10 -8 c)3.67 × 10 -7 d)3.67 × 10 -11 c) 3.67 × 10 -7

14. CONFIDENTIAL 14 6) A movie grossed nearly 6.7 × 10 6 dollars. What is this number in standard form. a)$0.000067 b)$6,700,000 c)$670,000 d)$67,000,000 b) $6,700,000

15. CONFIDENTIAL 15 7) A micrometer is 0.000001 meter. Which expression represents this number in scientific notation? a)1.0 × 10 7 meter b)1.0 × 10 6 meter c)1.0 × 10 -5 meter d)1.0 × 10 -6 meter

16. CONFIDENTIAL 16 8) What is 237 raised to the first power in the scientific notation? a)2.37 × 10 3 b)2.37 × 10 2 c)2.37 × 10 -2 d)2.37 × 10 -3 b) 2.37 × 10 2

17. CONFIDENTIAL 17 a)8 × (1.03) 8 b)8 × (1.03) 7 c)8 × (1.03) 6 d)8 × (1.03) 9 9) The cost of a movie ticket is $8, which increases by 3% each year. Find the cost of the ticket after 8 years. YearCost 18 × (1.03) 28 × (1.03) 2 38 × (1.03) 3 48 × (1.03) 4 a) 8 × (1.03) 8

18. CONFIDENTIAL 18 10) A teacher asked four students for the value of 4 × 10 3, Chris said 400, Ed said 4,000, Jake said 40,000 and Gary said 400,000. Who among the four is correct? a)Chris b)Ed c)Jake d)Gary b) Ed

19. Assessment

20. CONFIDENTIAL 20 1) What is the number 961400000 denoted as in the scientific notation? a)9.614× 10 8 b)9.614 × 10 -8 c)9.614 × 10 7 d)9.614 × 10- 7 a) 9.614× 10 8

21. CONFIDENTIAL 21 2) What is the number 7.03 × 10 -5 denoted as in the standard notation? a)0.00000703 b)0.000703 c)0.00703 d)0.0000703

22. CONFIDENTIAL 22 3) Jake wrote a guess of 7,800 for the number of of jar. What is this number in the scientific notation? a)7.8 × 10 -4 b)7.8 × 10 3 c)7.8 × 10 -2 d)7.8 × 10 1 b) 7.8 × 10 3

23. CONFIDENTIAL 23 4) A certain bacterium is approximately 1.8 × 10 -7 mm long. How is length expressed in standard notation? c) 0.00000018 mm. a)0.000018 mm b)0.0000018 mm c)0.00000018 mm d)0.0018 mm

24. CONFIDENTIAL 24 5) Which number is the larger than 5.8 × 10 -3 ? a)6 × 10 -4 b)5.8 × 10 -4 c)5 × 10 -3 d)5.9 × 10 -3

25. CONFIDENTIAL 25 6) Light takes about 5.4 × 10- 6 second to travel one mile. What is this number in standard form. a)0.0000054 b)0.000054 c)0.0000054 d)0.00000054 a) 0.0000054

26. CONFIDENTIAL 26 7) To write 3.18 × 10 -3 in standard notation, how many places will the decimal point move? b) 3 places to the left. a)3 places to the right. b)3 places to the left. c)4 places to the left. d)4 places to the right.

27. CONFIDENTIAL 27 8) What is 2×10 3 + 4×10 2 + 7×10 1 in the standard form? a)2470 b)24700 c)2407 d)247 a) 2470

28. CONFIDENTIAL 28 9) Rents in a particular area are increasing by 10% every year. Predict what would be the rent of the apartment after 2 years, if its rent is $100 per month now? a)$105 b)$110 c)$120 d)$121

29. CONFIDENTIAL 29 10) There are 20 elephants in a zoo. What will be their population after 2 years, if the population doubles each year? a)40 elephants b)80 elephants c)60 elephants d)20 elephants b) 80 elephants

30. You did a great job today!