Inferences and observations notes

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1 Inferences and observations notes a. An observation is: i. Example: The poster at the front of Ms. Stork s room has a picture of Einstein and a quote on it. This is an observation because you can literally see the poster and the quote. b. A qualitative observation is: i. Einstein is wearing a sweater in the poster. This is a qualitative observation because it uses words (wearing a sweater) and no numbers to describe what you are looking at. c. A quantitative observation is: i. Example: There are 17 words in the quote on the Einstein poster. This is a quantitative observation because it uses a number (17 words) to describe what you are looking at. d. An inference is: i. Example: Einstein said, Do not worry about your difficulties in mathematics. I can assure you that mine are still greater. This is an inference, because although the quote is written next to Einstein on the poster, you have not literally heard or seen him say those words. You had to go beyond seeing to infer that the quote is on the poster because Einstein said that quote. 1

2 Place value notes In the number 12, : The number 1 is in the place The number 2 is in the place The number 3 is in the place The number 4 is in the place The number 5 is in the place The number 6 is in the place The number 7 is in the place The number 8 is in the place The place values, in order go: Thousands Hundreds Tens Ones. Tenths Hundredths Thousandths Or, in other words,,. thousands hundreds tens ones tenths hundredths thousandths one thousand = 1,000 one hundred = ten = one = one tenth = 1/10 or 0.1 one hundredth = 1/ or 0.01 one thousandth = or Place values to the of the decimal point represent whole numbers. Place values to the right of the decimal point represent or. 2

3 Hundreds are times bigger than tens Tens are times bigger than ones Ones are times bigger than tenths Tenths are times bigger than hundredths Hundredths are times bigger than thousandths Each place value is than its neighbor to the right. Analyze the following numbers: 3.2 o The 3 is in the place o The 2 is in the place 32 (remember, there is an invisible decimal point after the 2, like this: 32. ) o The 3 is in the place o The 2 is in the place o 32 is times bigger than 3.2 When changing from 3.2 to 32, did the decimal point move right or left? 152 o The 1 is in the place 1,520 o The 5 is in the place o The 2 is in the place o The 1 is in the place o The 5 is in the place o The 2 is in the place o 1,520 is times bigger than 152 When changing from 152 to 1,520, did the decimal point move left or right? I notice that when the decimal point moves one place to the, the number. I predict that when the decimal point moves one place in the opposite direction, to the, the number will. 3

4 Exponents Notes We know how to calculate the expression 5 x 5. This expression can be written in a shorter way using something called exponents. An expression that represents repeated multiplication of the same factor is called a. The number 5 is called the, and the number 2 is called the. The exponent corresponds to the number of times the base appears in the repeated multiplication. Fill in the empty boxes in the chart below to the first power to the second power or 4 squared to the third power or 5 cubed Practicing powers of 10: Fill in the empty boxes in the chart below x I notice that, in powers of 10, the tells me how many zeros are at the end of the number. 4

5 A number with a negative exponent is the same as the reciprocal of the number with a positive exponent. Example: 4!! = 1 4! = Use your calculator as needed to answer the following questions: 1. 10!! =!!" = !! =!!"!" = = = I notice that, in negative powers of ten, the exponent tells me. Multiplying a number by 10 makes the number 10 times and so the decimal moves one place to the. Multiplying a number by 10-1 is like multiplying the number by 1/10, or dividing by 10. Multiplying a number by 10-1 makes the number 10 times and so the decimal moves one place to the. How many places do you think the decimal moves if you multiply a number by 10 3? Try it! 1, x 10 3 = How many places did the decimal move? Left or right? How many places do you think the decimal moves if you multiply a number by 10-3? Try it! 1, x 10-3 = How many places did the decimal move? Left or right? Based on what you just discovered: When you multiply a number by a positive power of ten, the exponent tells you. When you multiply a number by a negative power of ten, the exponent tells you. 5

6 Scientific Notation Notes 1. Scientific notation is: 2. The form for scientific notation is: 3. Rules for scientific notation: a. The coefficient: b. The base: c. The exponent 4. Positive exponents tell you: 5. Negative exponents tell you: 6. Scientific notation is useful because: 6

7 Scientific Notation Homework Explain, in full sentences, why the following numbers are not in scientific notation: x x x x 10 1/ x 5 20 Convert the following numbers from scientific notation to standard notation. You must show your work in order to receive credit!!! The first one is done as an example for you: x 10 5 = 482,800 work: x 10-2 = x = x 10-8 = x 10 4 = Challenge! (You must attempt all of the challenge problems) Convert the following numbers from standard notation to scientific notation. You must show your work in order to receive credit!!! 11. 1,320 = = 13. 1,598,000,000 = = ,781 = 7