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Teacher Notes Subject: Math Topic: Scientific Notation Title: Scientific Notation Grade(s): 6, 7and 8 Cross curricular

how multiply numbers written in scientific form Students learn how to write and multiply numbers less than one in scientific

developing and presenting lesson activities. 2004 SMART Technologies Inc. All rights reserved.

1 Teacher Notes Subject: Math Topic: Scientific Notation Title: Scientific Notation Grade(s): 6, 7and 8 Cross curricular link(s): Nonspecific Intended learning outcome(s) Students learn how to convert numbers to scientific notation Students learn how multiply numbers written in scientific form Students learn how to write and multiply numbers less than one in scientific notation Recommended usage: Introduction or review How to use Notebook(TM) software Learn helpful tips and tricks for developing and presenting lesson activities SMART Technologies Inc. All rights reserved. For further information, please see copyright notice. Scientific Notation Windows(R) operating system and Mac OS X operating system software Submitted by Candace Beaton 1

54) is called the coefficient. The coefficient must be greater than or equal to 1 and less than 10. The second number (10) is called the base.

2 What is scientific notation? Use the dictionary link provided and find the definition for scientific notation. Write the definition below. The number 154,000,000,000 is written in scientific notation as 1.54 x exponent coefficient base The first number (1.54) is called the coefficient. The coefficient must be greater than or equal to 1 and less than 10. The second number (10) is called the base. It must always be 10. The base number 10 is always written in exponent form. The third number (11) is called the exponent. It is also referred to as the power of t 2

3 Write this number in scientific notation by following the steps below. Put the decimal after the first digit Find the exponent by counting the number of places from the decimal to th end of the number Drop the zeros to get the coefficient. Multiply it by the base (which is always 10) and include the exponent that you found in step x 10 Write the following numbers in scientific notation using the steps provided on page

4 Complete the following table. Number Coefficient Base Exponent Fill in the blanks = x = x = x = x10 7 = 7.89 x10 = x10 9 4

2 = 6.72 Add the exponents together. (Base 10 always remains the same.) 8 + 4 = 12 Write the product. 8 4 12 (2.

5 Multiplication in scientific notation 8 4 (2.1 x 10 ) (3.2 x 10 ) Multiply these two numbers together by following the steps below. Multiply the coefficients together. 2.1 x 3.2 = 6.72 Add the exponents together. (Base 10 always remains the same.) = 12 Write the product (2.1 x 10 ) (3.2 x 10 ) = 6.72 x 10 Multiply the following using the steps provided on page (2 X 10 )(4 X 10 ) = 5 6 (3 X 10 )(2 X 10 ) = 7 4 (5.5 X 10 )(1.1 x 10 ) = 9 5 (2.6 X 10 )(3.1 x 10 ) = 5

6 What happens if the coefficient is more than 10? Example: (6 x 10 ) (4 x 10 ) = 24 x 10 The product value is not correctly written in scientific notation because the coefficient is not between 1 and 10. To make it correct, move the decimal point over to the left until the coefficient is between 1 and 10. For each place you move the decimal to the left, the exponent will be increased by one power of ten (6 x 10 ) (4 x 10 ) = 24 x 10 = 2.4 x 10 Multiply the following and put the product in proper scientific notation. 4 5 (9.2 x 10 ) (3.1 x 10 ) = 8 5 (4.5 x 10 ) (4.2 x 10 ) = 4 9 (7.11 x 10 ) (3 x 10 ) = 2 6 (8.3 x 10 ) (7.2 x 10 ) = 6

7 How do you do multiplication of scientific notation if the exponents are negative? When multiplying numbers in scientific notation that have negative exponents, use the same steps as before but use the rules of addition of signed numbers Example: (2 x 10 ) (3x 10 ) = 6 x 10 Multiply the following numbers: -6-4 (3 X 10 )(2X10 ) = -5 2 (5 X 10 )(1 X 10 ) = -7 4 (5.5 X 10 )(4.2 x 10 ) = (2.4 x 10 6 ) (1.2 x 10 2 ) Division in scientific notation Divide these two numbers by following the steps below. Step 1. Divide the two coefficients Subtract the exponents. (Base 10 always remains the same.) 6-2 = 4 Step 3. Write the quotient. 2 x

8 Use the three steps to solve these problems. (3.9 x 10 5 ) (1.3 x 10 3 ) (7.5 x 10 1 ) (2.5 x 10 4 ) Step 1. Step 1. Step 2. Step 2. Step 3. Step 3. What happens if the coefficient is less than 1? (2.5 x 10 4 ) (5 x 10 2 ) = 0.5 x 102 The quotient value is not correctly written in scientific notation because the coefficient is not between 1 and 10. To make it correct, move the decimal point over to the right until the coefficient is between 1 and 10. For each place you move the decimal to the right, the exponent will be decreased by one power of ten. (2.5 x 10 4 ) (5 x 10 2 ) = 0.5 x 102 = 5 x

9 Divide the following and put the product in proper scientific notation. (1.4 x 10 5 ) (7 x 10 3 ) (2.4 x 10 7 ) (6 x 10 2 ) (1.2 x 10-2 ) (1.5 x 10 2 ) Word problems associated with the division of scientific notation. 1. A pronghorn antelope can travel at a speed of 6 x 10 1 miles per hour. A snail can travel at a speed of 3 x 10-2 miles per hour. How many times the speed of a nsail is the speed a pronghorn antelope? 2. The mass of Mercury is 3 x kg. The mass of Jupiter is 1.8 x kg. How many times the mass of Mercury is the mass of Jupiter? 9

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UNIT 5 EXPONENTS NAME: PERIOD:

UNIT 5 EXPONENTS NAME: PERIOD: NAME: PERIOD: UNIT 5 EXPONENTS Disclaimer: This packet is your notes for all of unit 5. It is expected you will take good notes and work the examples in class with your teacher in pencil. It is expected