1. Copyright © Ed2Net Learning, Inc. 11 Grade 8 Scientific Notation

2. Copyright © Ed2Net Learning, Inc. 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. Copyright © Ed2Net Learning, Inc. 3 Exponents The "exponent" stands for how 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. Copyright © Ed2Net Learning, Inc. 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. Copyright © Ed2Net Learning, Inc. 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. Copyright © Ed2Net Learning, Inc. 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. Copyright © Ed2Net Learning, Inc. 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. Copyright © Ed2Net Learning, Inc. 8 Let us do some practice problems!

9. Copyright © Ed2Net Learning, Inc. 99 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. Copyright © Ed2Net Learning, Inc. 10 2) What is the number 1.512 × 10 6 denoted as in the standard form? a)1512000000 b)1512000 c)151200000 d)15120000

11. Copyright © Ed2Net Learning, Inc. 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

12. Copyright © Ed2Net Learning, Inc. 12 4) To write 3.18 ×10 7 in standard form, 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.

13. Copyright © Ed2Net Learning, Inc. 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

14. Copyright © Ed2Net Learning, Inc. 14 6) A movie grossed nearly $6.7 × 10 6. What is this number in standard form? a)$0.000067 b)$6,700,000 c)$670,000 d)$67,000,000

15. Copyright © Ed2Net Learning, Inc. 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. Copyright © Ed2Net Learning, Inc. 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

17. Copyright © Ed2Net Learning, Inc. 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

18. Copyright © Ed2Net Learning, Inc. 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

19. Copyright © Ed2Net Learning, Inc. 19 Assessment

20. Copyright © Ed2Net Learning, Inc. 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

21. Copyright © Ed2Net Learning, Inc. 21 2) What is the number 7.03 × 10 -5 denoted as in the standard form? a)0.00000703 b)0.000703 c)0.00703 d)0.0000703

22. Copyright © Ed2Net Learning, Inc. 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

23. Copyright © Ed2Net Learning, Inc. 23 4) A certain bacterium is approximately 1.8 × 10 -7 mm long. How is length expressed in standard notation? a)0.000018 mm b)0.0000018 mm c)0.00000018 mm d)0.0018 mm

24. Copyright © Ed2Net Learning, Inc. 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. Copyright © Ed2Net Learning, Inc. 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

26. Copyright © Ed2Net Learning, Inc. 26 7) To write 3.18 × 10 -3 in standard notation, how many places will the decimal point move? 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. Copyright © Ed2Net Learning, Inc. 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

28. Copyright © Ed2Net Learning, Inc. 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. Copyright © Ed2Net Learning, Inc. 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

30. Copyright © Ed2Net Learning, Inc. 30 You did a great job today!