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Scientific Notation

Scientific Notation. Write what is in green!. What we know!. Scientific notation is a short hand way to write very big or very small numbers Scientific Notation has two parts: Part A: is a # between 1 and 10 (usually has a decimal in it) Part B: a power of 10

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Scientific Notation

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  1. Scientific Notation Write what is in green!

  2. What we know! • Scientific notation is a short hand way to write very big or very small numbers • Scientific Notation has two parts: • Part A: is a # between 1 and 10 (usually has a decimal in it) • Part B: a power of 10 • The two parts are multiplied together (example: 4.3 x 104= 43000)   Scientific Notation Standard Notation

  3. A step by step guide for writing very big numbers in scientific notation • Step 1: look at your number • 450 000 • Step 2: figure out how many times you need to divide your number by 10 so that the answer will be between 1 and 10 (hint: decimal must move between the first two digits) • 450 000 ÷ 10 = 45 000.0 • 45 000.0 ÷ 10 = 4 500.00 • 4 500.00 ÷ 10 = 450.000 • 450.000 ÷ 10 = 45.0000 • 45.0000 ÷ 10 = 4.50000  this number is between 1 and 10 • Step 3: write down your number and count how many times you divided by 10, that is the number for your exponent of 10. • 4.5 x 105

  4. Hint: • Did you notice the pattern??? • 450 000 ÷ 10 = 45 000.0 • 45 000.0 ÷ 10 = 4 500.00 • 4 500.00 ÷ 10 = 450.000 • 450.000 ÷ 10 = 45.0000 • 45.0000 ÷ 10 = 4.50000 • What happened to the decimal point every time we divided by 10? • It moved one place to the left…so could we simply count the number of times we move the decimal place to the left to bring the decimal place to between the first two digits?

  5. So… • When determining the power of 10 we could count how many places we need to move the decimal place to put it between the first two digits. That number is our power of 10… • Lets try…put the following numbers into scientific notation: • 350 000 • 57 300 • 20 460 000 • 456 000 000 • 2 400 000

  6. Did you get… • 350 000 = 3.5 x 105 • 57 300 = 5.73 x 104 • 20 460 000 = 2.046 x 107 or 2.05 x 107 • 456 000 000 = 4.56 x 108 • 2 400 000 = 2.40 x 106

  7. Step by step guide for writing a number in scientific notation back to standard notation • Step 1: Look at your Number • 3.6 x 105 • Step 2: expand out your power of 10 • 3.6 x 10 x 10 x 10 x 10 x 10 • Step 3: multiply your answer • 3.6 x 10 = 36 • 36 x 10 = 360 • 360 x 10 = 3600 • 3600 x 10 = 36000 • 36000 x 10 = 360000 • Step 4: write out your answer • 3.6 x 105 = 360000

  8. Hint: • Did you notice a pattern??? • 3.6 x 10 = 36 • 36 x 10 = 360 • 360 x 10 = 3600 • 3600 x 10 = 36000 • 36000 x 10 = 360000 • What happened to the decimal point every time we multiplied by 10? • It moved one place to the right…so could we simply count the number of times we need to move the decimal place by looking at the power?

  9. So…lets try these • Write the following in standard notation • 5.6 x 103 • 6.78 x 106 • 7.945 x 102 • 5.93 x 109 • 1.7 x 1012

  10. Did you get?? • 5.6 x 103 = 5600 • 6.78 x 106 = 6 780 000 • 7.945 x 102 = 794.5 • 5.93 x 109 = 5 930 000 000 • 1.7 x 1012 = 1 700 000 000 000

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