Bell Ringer Scientific Notation Copyright Science Stuff Using

Bell Ringer

Scientific Notation Copyright © Science Stuff

Using Scientific Notation in Multiplication, Division, Addition and Subtraction Scientists must be able to use very large and very small numbers in mathematical calculations. As a student in this class, you will have to be able to multiply, divide, add and subtract numbers that are written in scientific notation. Here are the rules.

How to Use Scientific Notation • In scientific notation, a number is written as the product of two numbers…. . A coefficient and 10 raised to a power.

The number 4, 500 is written in scientific notation as ________. 4. 5 x 103 The coefficient is _______. 4. 5 The coefficient must be a number greater than or equal to 1 and smaller than 10. The power of 10 or exponent in this example is _____. 3 The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4, 500.

Rules to Remember! If a number is greater than 10, the exponent will be _____ and is equal to positive the number of places the decimal must be moved to the _____ to write the left number in scientific notation.

Rules to Remember! If a number is less than 1, the exponent will be ______ and is equal to negative the number of places the decimal must be moved to the _______ to write the right number in scientific notation.

A number will have an exponent of zero if: …. the number is equal to or greater than 1, but less than 10.

To write a number in scientific notation: 1. Move the decimal to the right of the first non-zero number. 2. Count how many places the decimal had to be moved. 3. If the decimal had to be moved to the right, the exponent is negative. 4. If the decimal had to be moved to the left, the exponent is positive. To emphasize again: The exponent counts how many places you move the decimal to the left or right.

***VERY IMPORTANT*** When computing with Scientific Notation, sometimes you have to change the exponent. To do so, count how many times you need to move the decimal. à If you move the decimal forward, ADD that number to the exponents. à If you move the decimal backward, SUBTRACT that number to the exponents

Write as Scientific Notation 1) 0. 00012 2) 1000 3) 0. 01 4) 12 5) 0. 987

Write as Scientific Notation 1) 1. 2 x 10 -4 2) 1 x 103 3) 1 x 10 -2 4) 1. 2 x 101 5) 9. 87 x 10 -1

Write as Whole Number or Decimal 1) 4. 9 x 102 2) 3. 75 x 10 -2 3) 5. 95 x 10 -4 4) 9. 46 x 103 5) 3. 87 x 101

Write as Whole Number or Decimal 1) 490 2) 0. 0375 3) 0. 000595 4) 9460 5) 38. 7

Rule for Multiplication When multiplying numbers written in scientific notation…. . Step 1: Multiply the decimal numbers Step 2: Add the exponents (follow Exponent Rule) Step 3: Make sure you have one digit (non zero) in front of the decimal

Guided Practice (8. 4 x 2. 5) = 21 (102 x 106) = 108 (21 x 108) (2. 1 x 109)

Guided Practice (2. 63 x 2. 5) = 6. 575 (102 x 10 -4) = 10 -2 (6. 575 x 10 -2)

Rule for Division When dividing numbers written in scientific notation… Step 1: Divide the decimal numbers Step 2: Subtract exponents (follow Exponent rules) Step 3: Make sure you have one digit (non zero) in front of the decimal

Guided Practice (1. 2 ÷ 2. 4) = 0. 5 (107 ÷ 103) = 107 -3 = 104 (0. 5 x 104) (5. 0 x 104)

Guided Practice (4. 64 ÷ 2. 9) = 1. 6 (10 -4 x 10 -6) = 10 -4 -(-6) = 102 (1. 6 x 102)

Rule for Addition and Subtraction To add or subtract numbers written in scientific notation, you must…. express them with the same power of ten. Step 1: Make sure that both exponents are the SAME! ** you might have to move a decimal forward or backward to have same exponent #s Step 2: Add coefficients decimal #’s together Step 3: Make sure it is in SCIENTIFIC NOTATION!

Example (6. 89 + 92. 4) = 99. 29 (99. 29 x 104) (9. 929 x 104)

Example: Graphic Organizer (103 – 4. 7) = 98. 3 (98. 3 x 107) (9. 83 x 108)

Guided Practice: Adding (worksheet) (0. 593 + 7. 89) = 8. 483 (8. 483 x 106)