Mod 1: Pt 2: Scientific Notation

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1 Mod 1: Pt 2: Scientific Notation Name 1 P a g e

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4 Write the coefficient on the line provided 5.22 x x x x x x x x x x 10-4 Write the power of ten (exponent) on the line provided 5.22 x x x x x x x x x x x x x x P a g e

5 Using Magnitude to estimate numbers Directions: Make a guess of the number. Then, decide which power of ten the number would be closest to. For example: How many jolly ranchers are in a bag this size? My guess is 350 jolly ranchers. That number is closer to 100 than 1,000. Therefore, my closest power of ten would be The amount of cells in your finger 5 P a g e

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7 Part 1: Convert each number into scientific notation. ***Remember, all coefficients need to be between Example: 9,230 1) First I place the decimal between the 9 and the 2 (because 9.2 is between 1-10) 2) Then, I count the number of places the decimal has moved. In this case, it moved 3 times to the right 3) Because the decimal moved to the right, I know my exponent will be positive 4) My answer will be 9.23 x 10 3 Part 2: Convert each number into standard form. *****Remember, positive exponents will be large numbers and negative exponents will be very small numbers. Example: 4.56 x ) First I see if the exponent is positive or negative. Since it is positive, I will move my decimal to the right. 2) Second, I move the decimal the same number of places as the exponent tells me. 3). Third, I write in zeros as place holders. 4) My answer will be 4,560, P a g e

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9 Using Number Lines with Scientific Notation Timothy does not know where to put 9,898 on a number line Place.0006 on the number line Place 87 on the number line Place 45,654 on the number line Place.0008 on the number line Place 1,567 on the number line Place 1,000,000 on the number line 9 P a g e

10 Word problems Directions: Read the problem and write the numbers in either scientific notation or standard notation. 1) The biggest iceberg ever seen that had split off the Ross Ice Shelf in Antarctica happened during the spring of It was estimated to weigh about 4,000,000,000,000 tons. Write its weight in scientific notation. 2) The average distance between the Earth and the Sun is 92,960,000 miles. Write this distance in scientific notation. 3) The population of Texas was about 20,900,000 in the 2000 U.S. census. Write this number in scientific notation. 4) Willie Mays hit 6.6 x 10 2 home runs in his baseball career. Write this number in standard form. 5) The mass of Earth is about 6,580,000,000,000,000,000,000 tons. Write this value in scientific notation. 6) In 2001, the population of the world was about 6,160,000,000. The estimated population of the world for the year 2025 is 7,840,000,000. Write these values in scientific notation P a g e

11 Operations ADDING AND SUBTRACTING Note: In order to add or subtract numbers in scientific notation, the powers of ten need to be the same. 11 P a g e

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13 Multiplying using scientific notation Use the commutative property to rewrite the problem multiplying the coefficients together and the powers of ten together Multiply the coefficients. Since the powers of ten have the same bases, you can add the exponents This is not in scientific notation because is larger than 10!!! I have to move the decimal back to the left one space. This will change the exponent from 5 to 6. Examples: 13 P a g e

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15 Dividing Numbers in Scientific Notation Step 1 Step = Step = 10 5 Step x 10 5 = 2 x 10 4 Step 1: Write the problem as two (2) different division problems. Step 2: Divide the coefficients and write down your answer. Step 3: Using the quotient rule of exponents, subtract the exponents of the powers of ten Step 4: Rewrite in scientific notation (all coefficients must be between 1-10) Practice: 15 P a g e

16 Dividing using scientific notation Note: Divide the coefficients Use the law of exponents to divide the powers of ten Rewrite in scientific notation coefficient must between between P a g e

17 Review of the unit Convert to scientific notation , Convert to standard form 5.66 x x x x 10 5 Place these numbers on the number lines 9, Word Problems In 2004, the richest man in the world s assets were estimated at about $90,000,000,000. Write this value in scientific notation Lebron James makes 2.4 x 10 6 dollars per year playing basketball. Write that value of dollars in standard form. 17 P a g e

18 Operations with Scientific Notation Adding and subtracting Multiplying and Dividing 18 P a g e

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