Working with Exponents and Scientific Notation

# Working with Exponents and Scientific Notation

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## Working with Exponents and Scientific Notation

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1. Today’s Lesson Working with Exponents and Scientific Notation

2. Warm-Up Activity We will warm up today by working with volume.

3. How do you find the volume of the box?

4. Volume of the rectangular prism = length x width x height V = lwh height width length

5. x = 2 5 4 • • V = lwh x = 40 in.3

6. V = lwh • • 60 = x34 • • How can you find the missing variable? 60 = 12x x = 5 in.

7. V = l w h • • 84 = 7 x3 • • How can you find the missing variable? 84 = 21x 4 ft. = x

8. Find the unknown variables.

9. Whole-Class Skills Lesson Today you will be working with exponents to write numbers in scientific notation.

10. What is another way to write 3∙3∙3∙3? 3∙3∙3∙3 = 34 34 = 81

11. exponent power 34 = 81 base

12. What is a base? The base is the factor that you multiply. What is an exponent? The exponent tells how many times to multiply the base. What is a power? The result of multiplying the base.

13. How do you write these expressions in exponent form? 3∙3∙3∙3∙3∙3 36 5∙5∙5∙5 54 52∙52∙52 523

14. Scientific Notation 3,500,000 3.5 x 106 The first term must be greater than or equal to 1 but also less than 10. The exponent tells how many places to move the decimal.

15. Scientific Notation 900,000 Where is the decimal point? Which direction do you move the decimal point when writing the whole number in scientific notation? How many places does the decimal point move? 9.0 x 105

16. Write the numbers below in scientific notation. 5,600 5.6 x 103 125,000 1.25 x 105 7,500,000 7.5 x 106 34,000 3.4 x 104

17. What pattern do you see? 33 = 27 32 = 9 31 = 3 30 = 1 3–1 = 3–2 = 3–3 =

18. What happens to the exponents as you move from 33 to 3–3? 33 = 27 32 = 9 The exponent is decreasing by 1. 31 = 3 30 = 1 What happens to the powers as you move from 33 to 3–3? 3–1 = The powers are being divided by 3. 3–2 = 3–3 =

19. Scientific Notation 0.0000042 Where is the decimal point? Which direction do you move the decimal point when writing the whole number in scientific notation? How many places does the decimal point move? 4.2 x 10–6

20. Write the numbers below in scientific notation. 0.0032 3.2 x 10–3 5.6 x 10–2 0.056 9.8 x 10–6 0.0000098 0.00071 7.1 x 10–4

21. Write 94,000 in scientific notation. Remember the first number must be a number greater than 1 but less than 10. How many places do we need to move the decimal? 9.4 x 104

22. Write the numbers below in scientific notation. How do you solve the problems? 7.29 x 10–3 0.00729 2.25 x 103 2,250 4.23 x 105 423,000 6.3 x 10–4 0.00063

23. Write each number in scientific notation. 7.1 x 10,000 7.1 ∙ 104 7.1 ∙ 10 ∙ 10 ∙ 10 ∙ 10