Purpose of Magnitude Scientific Notation Comparing Numbers in - PDF document

Slide 1 / 137 Slide 2 / 137 8th Grade Scientific Notation 2015-11-20 www.njctl.org Slide 3 / 137 Slide 4 / 137 Table of Contents Click on the topic to go to that section Purpose of Scientific Notation · Writing Numbers in Scientific Notation · Converting Between Scientific Notation and Standard Form · Purpose of Magnitude · Scientific Notation Comparing Numbers in Scientific Notation · Multiply and Divide with Scientific Notation · Addition and Subtraction with Scientific Notation · Glossary · Return to Table of Contents Slide 5 / 137 Slide 6 / 137 Can you match these Purpose of Scientific Notation BIG objects to their weights? The Earth The Great Pyramid at Giza Scientists are often confronted with numbers that look like this: 300,000,000,000 kg 300,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000 kg 2,000,000,000,000,000,0 00,000,000,000,000 kg Can you guess what weighs this much? Blue Whale - largest animal on earth 600,000,000 kg 60,000,000,000,000, The Sun 000,000,000,000 kg Total Human Population 180,000 kg

Slide 7 / 137 Slide 8 / 137 grain of sand Can you match these Can you match these small BIG objects to their weights? objects to their weights? The Earth The Great Pyramid at Giza Click object to reveal 600,000,000 kg answer 60,000,000,000,000, molecule 000,000,000,000 kg 0.00015 kg Blue Whale - largest animal on earth 0.000000000000000000000000030 kg 180,000 kg 0.00000000035 kg steam The Sun Total Human Population 2,000,000,000,000,000,0 00,000,000,000,000 kg 300,000,000,000 kg Slide 9 / 137 Slide 10 / 137 grain of sand Scientific Notation Click to reveal the answers. The examples were written in standard form , the form we 0.00000000035 kg normally use. But the standard form is difficult to work with when a number is HUGE or tiny , if it has a lot of zeros. molecule Scientists have come up with a more convenient method to write very LARGE and very small numbers. 0.000000000000000000000000030 kg Writing numbers in scientific notation doesn't change the value of the number. steam 0.00015 kg Slide 11 / 137 Slide 12 / 137 Scientific Notation Powers of Ten 10 1 = 10 Scientific Notation uses Powers of 10 to write big or small 10 2 = 10 x 10 = 100 numbers more conveniently. 10 3 = 10 x 10 x 10 = 1,000 10 4 = 10 x 10 x 10 x 10 = 10,000 Using scientific notation requires us to use the rules of exponents we learned earlier. While we developed those 10 5 = 10 x 10 x 10 x 10 x 10 = 100,000 rules for all bases , scientific notation only uses base 10. Click here to see a video on powers of ten which puts our universe into perspective! Click here to move from the Milky Way through space towards Earth to an oak tree, and then within a cell!

Slide 13 / 137 Slide 14 / 137 Powers of Integers Review of Exponent Rules Remember that when multiplying numbers with Powers are a quick way to write repeated multiplication, just as exponents, if the bases are the same, you write multiplication was a quick way to write repeated addition. the base and add the exponents. These are all equivalent: 2 5 x 2 6 = 2 (5+6) = 2 11 10 3 3 3 x 3 7 = 3 (3+7) = 3 10 (10)(10)(10) 1000 10 8 x 10 -3 = 10 (8+-3) = 10 5 In this case, the base is 10 and the exponent is 3. 4 7 x 4 -7 = 4 (7+-7) = 4 0 = 1 Slide 15 / 137 Slide 16 / 137 10 2 x 10 4 = 10 14 x 10 -6 = 1 2 A 10 6 A 10 6 B 10 8 B 10 8 C 10 10 C 10 10 D 10 12 D 10 12 Slide 17 / 137 Slide 18 / 137 3 10 -4 x 10 -6 = 4 10 4 x 10 6 = A 10 -6 A 10 6 B 10 -8 B 10 8 C 10 -10 C 10 10 D 10 -12 D 10 12

Slide 19 / 137 Slide 20 / 137 Scientific Notation Here are some different ways of writing 6,500. 6,500 = 6.5 thousand 6.5 thousand = 6.5 x 1,000 Writing Numbers in 6.5 x 1,000 = 6.5 x 10 3 Scientific Notation which means that 6,500 = 6.5 x 10 3 6,500 is standard form of the number and 6.5 x 10 3 is scientific notation These are two ways of writing the same number. Return to Table of Contents Slide 21 / 137 Slide 22 / 137 Scientific Notation Scientific Notation 6.5 x 10 3 isn't a lot more convenient than 6,500. Scientific notation expresses numbers as the product of: a coefficient and 10 raised to some power. But let's do the same thing with 7,400,000,000 3.78 x 10 6 which is equal to 7.4 billion which is 7.4 x 1,000,000,000 The coefficient is always greater than or equal to one, and less than which is 7.4 x 10 9 10. In this case, the number 3,780,000 is expressed in scientific notation. Besides being shorter than 7,400,000,000 it is a lot easier to keep track of the zeros in scientific notation. And we'll see that the math gets a lot easier as well. Slide 23 / 137 Slide 24 / 137 Express 870,000 in Scientific Notation Express 53,600 in Scientific Notation 1. Write the number without the comma. 870000 1. Write the number without the comma. 2. Place the decimal so that the first number will be less than 10 but 2. Place the decimal so that the first 8 . 70000 x 10 greater than or equal to 1. number will be less than 10 but greater than or equal to 1. 3. Count how many places you had to move the decimal point. This 3. Count how many places you had 8 . 70000 x 10 becomes the exponent of 10. to move the decimal point. This 5 4 3 2 1 becomes the exponent of 10. 4. Drop the zeros to the right of the right-most non-zero digit. 4. Drop the zeros to the right of the 8.7 x 10 5 right-most non-zero digit.

Slide 25 / 137 Slide 26 / 137 Express 284,000,000 in Scientific Notation 5 Which is the correct coefficient of 147,000 when it is written in scientific notation? 1. Write the number without the comma. A 147 2. Place the decimal so that the first B 14.7 number will be less than 10 but greater than or equal to 1. C 1.47 D .147 3. Count how many places you had to move the decimal point. This becomes the exponent of 10. 4. Drop the zeros to the right of the right-most non-zero digit. Slide 27 / 137 Slide 28 / 137 6 Which is the correct coefficient of 23,400,000 7 How many places do you need to move the when it is written in scientific notation? decimal point to change 190,000 to 1.9? A .234 A 3 B 2.34 B 4 C 234. C 5 D 23.4 D 6 Slide 29 / 137 Slide 30 / 137 8 How many places do you need to move the 9 Which of the following is 345,000,000 in scientific notation? decimal point to change 765,200,000,000 to 7.652? A 3.45 x 10 8 A 11 B 3.45 x 10 6 B 10 C 345 x 10 6 C 9 D .345 x 10 9 D 8

Slide 31 / 137 Slide 32 / 137 The Mass of the Solar System 10 Which of these numbers, written in scientific notation, is not a number greater than one? A .34 x 10 8 300,000,000,000,000, 000,000,000,000,000, B 7.2 x 10 3 000,000,000,000,000, 000,000,000 kg C 8.9 x 10 4 D 2.2 x 10 -1 (How do you even say that E 11.4 x 10 12 number?) F .41 x 10 3 Slide 33 / 137 Slide 34 / 137 Express 9,040,000,000 in Scientific Notation 1. Write the number without the comma. 2. Place the decimal so that the first More Practice number will be less than 10 but greater than or equal to 1. 3. Count how many places you had to move the decimal point. This becomes the exponent of 10. 4. Drop the zeros to the right of the right-most non-zero digit. Slide 35 / 137 Slide 36 / 137 Express 13,030,000 in Scientific Notation Express 1,000,000,000 in Scientific Notation 1. Write the number without the comma. 1. Write the number without the comma. 2. 2. Place the decimal so that the first Place the decimal so that the first number will be less than 10 but number will be less than 10 but greater than or equal to 1. greater than or equal to 1. 3. 3. Count how many places you had Count how many places you had to move the decimal point. This to move the decimal point. This becomes the exponent of 10. becomes the exponent of 10. 4. Drop the zeros to the right of the 4. Drop the zeros to the right of the right-most non-zero digit. right-most non-zero digit.

Slide 37 / 137 Slide 38 / 137 11 Which of the following is 12,300,000 in scientific 12 The average distance from Earth to the Moon is notation? approximately 384,400,000 meters. What is the average distance, in kilometers, from Earth to the Moon written in A .123 x 10 8 scientific notation? B 1.23 x 10 5 3.844 x 10 4 kilometers A C 123 x 10 5 B 3.844 x 10 5 kilometers D 1.23 x 10 7 C 3.844 x 10 7 kilometers D 3.844 x 10 8 kilometers From PARCC PBA sample test calculator #1 Slide 39 / 137 Slide 40 / 137 13 The closest that Venus ever gets to Earth is 38,000,000 km. What is this distance, in meters, from Venus to Earth written in scientific notation? A 3.8 x 10 9 kilometers Writing Small Numbers in B 3.8 x 10 7 kilometers Scientific Notation C 3.8 x 10 10 kilometers 3.8 x 10 6 kilometers D Slide 41 / 137 Slide 42 / 137 Express 0.00000832 in scientific notation Express 0.0043 in Scientific Notation 1. Write the number without the decimal point. 0043 1. Write the number without the decimal point. ? 2. Place the decimal so that the first number 2. Place the decimal so that the first number 004.3 x 10 is 1 or more, but less than 10. is 1 or more, but less than 10. 004.3 x 10 ? 3. 3. Count how many places you had to move Count how many places you had to move the decimal point. The negative of this the decimal point. The negative of this 123 number becomes the exponent of 10. numbers becomes the exponent of 10. 4. 4. Drop the zeros to the left of the left-most Drop the zeros to the left of the left-most 4.3 x 10 -3 non-zero digit. non-zero digit.