Warm-Up 9/12/13 Write down the following pairs of numbers: 3.2 x 104 and 32,000 .0000047 and 4.7 x 10-6 65,000,000 and 6.5 x 107 Use <, >, or = to compare the value of the numbers. Use your table partners for help, and make your best guess if you are unsure!

Scientific Notation Thursday 9/12/13

Why Scientific Notation? Used to express very large numbers and extremely small numbers in a shortened form. Examples (from warm-up): 3.2 x 104 = 32,000 .0000047 = 4.7 x 10-6 65,000,000 = 6.5 x 107

Scientific to Standard Form From scientific notation, we can determine the original form of the number. The exponent tells you how many times to move the decimal to get back to “standard” form. 102 is the same as 10x10, or moving the decimal right twice 104 is the same as 10x10x10x10 or moving the decimal right four times

Two Types of Exponents Positive Negative Ex) 6.7 x 105 Rule for Re-writing: If an exponent is positive, the number gets larger, so move the decimal to the right. Ex) 6.7 x 10-5 Rule for Rewriting: If an exponent is negative, the number gets smaller, so move the decimal to the left.

Examples What is 8.2 x 105 in standard form? +5 exponent means multiplying by 10 five times! OR moving decimal right five times. 8.20000. 820,000 What is 1.3 x 10-4 in standard form? -4 exponent signals the standard form number is small. We move the decimal left four times. .0001.3 .00013

Try These! Change these numbers to standard form (you have one minute!) 9.7 x 10-6 4.4 x 109 .0000097 4,400,000,000

Standard to Scientific Notation To put a number into scientific notation: Move the decimal until there is one digit (1-9) in front of it. 410,000 becomes 4.10000 or 4.1 Take the number from step 1, and add x10 after it. 4.1 x 10

Count the number of times you had to move the decimal in step 1 Count the number of times you had to move the decimal in step 1. This is the value of the exponent. 4.1 x 10 5 If you moved right, the exponent is negative. If you moved left, the exponent is positive. 4.1 x 10+5

5.5 x 10-4 (we moved right, so negative exponent) Another Example Write .00055 in scientific notation. 5.5 5.5 x 10 5.5 x 104 5.5 x 10-4 (we moved right, so negative exponent)

Your Job With one other person, complete the matching activity. Cut out all cards Match the standard and scientific form Match the sets of numbers to the object that is closest to that size (You should have three cards in each set) When done, check your answers with me  I’m checking for Metric Basics and Metric Mania HW assignments while you work!