Factor Vocab Word 2 Its meaning (As it is used Scientists are - PDF document

Slide 1 / 127 Slide 2 / 127 Scientific Notation 8th Grade 2014-10-27 www.njctl.org Slide 3 / 127 Slide 4 / 127 Vocabulary words are identified with a Table of Contents dotted underline. Click on the topic to go to that section · The purpose of scientific notation Sometimes when you subtract the fractions, you find that you can't because the first · How to write numbers in scientific notation numerator is smaller than the second! When this happens, you need to regroup from the How to convert between scientific notation 
 · whole number. (Click on the dotted and standard form underline.) · Magnitude How many thirds are in 1 whole? · Comparing numbers in scientific notation How many fifths are in 1 whole? · Multiply and Divide with scientific notation How many ninths are in 1 whole? · Addition and Subtraction with scientific notation Glossary · The underline is linked to the glossary at the end of the Notebook. It can also be printed for a word wall. Slide 5 / 127 Slide 6 / 127 The charts have 4 parts. 1 Purpose of Scientific Notation Factor Vocab Word 2 Its meaning (As it is used Scientists are often confronted with numbers that look like this: A whole number A whole number that can divide into that multiplies with in the another number another number to 300,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, lesson.) with no remainder. make a third number. 000 kg 5 .1 Can you guess what weighs this much? R 15 3 5 3 16 3 is a factor of 15 3 is not a 3 x 5 = 15 factor of 16 3 Back to 3 and 5 are 4 Instruction factors of 15 Return to Examples/ Table of Link to return to the Counterexamples Contents instructional page.

Slide 7 / 127 Slide 8 / 127 Can you match these BIG objects Can you match these BIG objects to their weights? to their weights? The Great Pyramid at Giza The Great Pyramid at Giza The Earth The Earth 600,000,000 kg 300,000,000,000 kg 60,000,000,000,000, 000,000,000,000 kg 2,000,000,000,000,000, Blue Whale - largest animal on earth Click object Blue Whale - largest animal on earth 000,000,000,000,000 kg to reveal 180,000 kg answer 600,000,000 kg The Sun 60,000,000,000,000, The Sun Total Human Population 000,000,000,000 kg Total Human Population 2,000,000,000,000,000, 300,000,000,000 kg 000,000,000,000,000 kg 180,000 kg Slide 9 / 127 Slide 10 / 127 Can you match these small Click to reveal answers. objects to their weights? grain of sand grain of sand 0.00015 kg 0.00000000035 kg molecule molecule 0.000000000000000000000000030 kg 0.000000000000000000000000030 kg steam steam 0.00000000035 kg 0.00015 kg Slide 11 / 127 Slide 12 / 127 Scientific Notation Scientific Notation The examples were written in "standard form", the form we Scientific Notation uses Powers of 10 to write big or small normally use. But the standard form is difficult to work with numbers more conveniently. when a number is HUGE or tiny , if it has a lot of zeros. Using scientific notation requires us to use the rules of Scientists have come up with a more convenient method to exponents we learned earlier. While we developed those write very LARGE and very small numbers. rules for all bases, scientific notation only uses base 10. Writing numbers in scientific notation doesn't change the value of the number.

Slide 13 / 127 Slide 14 / 127 Powers of Ten Powers of Integers 10 1 = 10 Powers are a quick way to write repeated multiplication, 10 2 = 10 x 10 = 100 just as multiplication was a quick way to write repeated addition. 10 3 = 10 x 10 x 10 = 1,000 10 4 = 10 x 10 x 10 x 10 = 10,000 These are all equivalent: 10 5 = 10 x 10 x 10 x 10 x 10 = 100,000 10 3 (10)(10)(10) 1000 click here to see a video on powers of ten which puts our universe into perspective! In this case, the base is 10 and the exponent is 3. click here to move from the Milky Way through space towards Earth to a oak tree, and then within a cell ! Slide 15 / 127 Slide 16 / 127 Exponent Rules 1 10 2 x 10 4 = Remember that when multiplying numbers with exponents, if A 10 6 the bases are the same, you write the base and add the exponents. B 10 8 Answer 2 5 x 2 6 = 2 (5+6) = 2 C 10 10 11 D 10 12 (3+7) = 3 3 3 x 3 7 = 3 10 10 8 x 10 -3 = 10 = 10 (8+-3) 5 4 7 x 4 -7 = 4 (7+-7) = 4 0 = 1 Slide 16 (Answer) / 127 Slide 17 / 127 1 10 2 x 10 4 = 2 10 14 x 10 -6 = 10 6 10 6 A A B 10 8 B 10 8 Answer C 10 10 C 10 10 A Answer D 10 12 D 10 12 [This object is a pull tab]

Slide 17 (Answer) / 127 Slide 18 / 127 2 10 14 x 10 -6 = 3 10 -4 x 10 -6 = 10 6 10 -6 A A B 10 8 B 10 -8 Answer C 10 10 C 10 -10 Answer B D 10 12 D 10 -12 [This object is a pull tab] Slide 18 (Answer) / 127 Slide 19 / 127 3 10 -4 x 10 -6 = 4 10 4 x 10 6 = A 10 -6 A 10 6 B 10 -8 B 10 8 Answer Answer C 10 -10 C 10 10 C D 10 -12 D 10 12 [This object is a pull tab] Slide 19 (Answer) / 127 Slide 20 / 127 4 10 4 x 10 6 = 10 6 A B 10 8 Writing Numbers Answer C 10 10 in Scientific C Notation D 10 12 [This object is a pull tab] Return to Table of Contents

Slide 21 / 127 Slide 22 / 127 Scientific Notation Here are some different ways of writing 6,500. 6,500 = 6.5 thousand Writing Large 6.5 thousand = 6.5 x 1,000 Numbers in 6.5 x 1,000 = 6.5 x 10 3 Scientific Notation which means that 6,500 = 6.5 x 103 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. Slide 23 / 127 Slide 24 / 127 Scientific Notation Scientific Notation Scientific notation expresses numbers as the product of: 6.5 x 10 3 isn't a lot more convenient than 6,500. But let's do the same thing with 7,400,000,000 which is equal to 7.4 billion a coefficient and 10 raised to some power . which is 7.4 x 1,000,000,000 which is 7.4 x 10 9 3.78 x 10 6 Besides being shorter than 7,400,000,000 it is a lot easier to keep track of the zeros in scientific notation. The coefficient is always greater than or equal to one, and less than 10. And we'll see that the math gets a lot easier as well. In this case, the number 3,780,000 is expressed in scientific notation. Slide 25 / 127 Slide 26 / 127 Express 53,600 in scientific notation Express 870,000 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 greater than or equal 2. Place the decimal so that the first number Answer . 870000 x 10 to 1. 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 3. Count how many places you had to move . 870000 x 10 of 10. the decimal point. This becomes the exponent of 10. 5 4 3 2 1 4. Drop the zeros to the right of the right-most non-zero digit. 4. Drop the zeros to the right of the right-most 8.7 x 10 5 non-zero digit.

Slide 26 (Answer) / 127 Slide 27 / 127 Express 53,600 in scientific notation Express 284,000,000 in scientific notation 1. Write the number without the comma. 1. Write the number without the comma. 2. Place the decimal so that the first number 2. Place the decimal so that the first number will be less than 10 but greater than or equal will be less than 10 but greater than or equal Answer Answer to 1. to 1. 5.36 x 10 4 3. Count how many places you had to move 3. Count how many places you had to move the decimal point. This becomes the exponent the decimal point. This becomes the exponent of 10. of 10. 4. Drop the zeros to the right of the right-most 4. Drop the zeros to the right of the right-most [This object is a pull tab] non-zero digit. non-zero digit. Slide 27 (Answer) / 127 Slide 28 / 127 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. 2. Place the decimal so that the first number A 147 will be less than 10 but greater than or equal B 14.7 to 1. Answer Answer 2.84 x 10 8 C 1.47 3. Count how many places you had to move the decimal point. This becomes the exponent D .147 of 10. 4. Drop the zeros to the right of the right-most non-zero digit. [This object is a pull tab] Slide 28 (Answer) / 127 Slide 29 / 127 5 Which is the correct coefficient of 147,000 when it is 6 Which is the correct coefficient of 23,400,000 written in scientific notation? when it is written in scientific notation? A 147 A .234 B 14.7 B 2.34 Answer Answer C 1.47 C C 234. D .147 D 23.4 [This object is a pull tab]

Slide 29 (Answer) / 127 Slide 30 / 127 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 Answer Answer B C 234. C 5 D 23.4 D 6 [This object is a pull tab] Slide 30 (Answer) / 127 Slide 31 / 127 8 How many places do you need to move the 7 How many places do you need to move the decimal point to change 765,200,000,000 to 7.652? decimal point to change 190,000 to 1.9? A 3 A 11 B 4 B 10 Answer Answer C C 5 C 9 D 6 D 8 [This object is a pull tab] Slide 31 (Answer) / 127 Slide 32 / 127 8 How many places do you need to move the 9 Which of the following is 345,000,000 in scientific decimal point to change 765,200,000,000 to 7.652? notation? A 11 A 3.45 x 10 8 B 10 B 3.45 x 10 6 Answer Answer A C 9 C 345 x 10 6 D 8 D .345 x 10 9 [This object is a pull tab]