Fun with numbers: Scientific Notation

There are about 6 billion people on earth. That’s 6,000,000,000. The number of cells in a person’s body is about 50 trillion. That’s 50,000,000,000,000. The mass of a single proton is 0.000000000000000000000000001.67

How about this one? The sun contains about two decillion grams of hydrogen. 2,000,000,000,000,000,000,000, 000,000,000,000. 2 with 33 zeroes after it!

That’s too much to work with That’s too much to work with! That’s why we use scientific notation in chemistry. We use scientific notation to express numbers that are extremely large or extremely small.

Expressing in scientific notation: The form is N x 10x where N is a number greater than 1 but less than 10, and x is the exponent.

Which of these numbers is in scientific notation. A. 5. 0 x 103 B Which of these numbers is in scientific notation? A. 5.0 x 103 B. 0.5 x 104 How do we know? Because 5.0 is greater than 1, but less than 10 and 0.5 is not!

Putting numbers into scientific notation: 5,000,000 Move the decimal point behind the first number greater than 0. That number becomes your coefficient (but you can drop extra zeros). The number of times you moved the decimal point becomes the exponent. So 5,000,000 in scientific notation is 5.0 x 106

Practice: Convert 1,234,000,000 into scientific notation. 1.234 x 109

Scientific notation helps with small numbers too! 0.00000002

Scientific Notation of very small numbers 0.00000002 is 2 x 10-8 The “-” means the number in standard notation was less than one. We had to move the decimal to the right.

Let’s Practice 6400: ___________________________ 6.4 x 103 6400: ___________________________ 0.000 000 0452: __________________ 0.000 005 600: ___________________ 3,430,000,000,000: ________________ 232,000: ________________________ 0.001 320: _______________________ 6.4 x 103 4.52 x 10-8 5.6 x 10-6 3.43 x 1012 2.32 x 105 1.320 x 10-3

Scientific Notation to Standard Notation If the exponent is positive, move the decimal point that many places to the right. 7.68 x 108 = 7.68000000 = 768,000,000 If the exponent is negative, move the decimal point that many places to the left. 3.99 x 10-5 = 3.99 = 0.0000399

Let’s Practice 6.41 X 10-11: _____________________ 0.000 000 000 064 1 0.000 866 105,000,000,000,000 0.000 000 004 25 98,700 50,800,000,000

Adding and Subtracting Step 1: Adjust the powers of 10 in the 2 numbers so that they are the same. (Tip: It is easier to adjust the smaller power to equal the larger power). (Tip: One will not be in true scientific notation) Step 2 : Add or subtract the numbers. Step 3 : Give the answer in scientific notation.

= .20 x 10³ + 3.0 x 10³ 2.0 x 10² + 3.0 10³ Step 1: Adjust the powers of 10 in the 2 numbers so that they are the same. (Tip: It is easier to adjust the smaller power to equal the larger power). (Tip: One will not be in true scientific notation) Step 2 : Add or subtract the numbers. Step 3 : Give the answer in scientific notation. .2 x 10³ + 3.0 x 10³ = (.2+3) x 10³ = 3.2 x 10³ 2.0 x 107 - 6.3 x 105 2.0 x 107 -.063 x 107 = (2.0-.063) x 107 = 1.937 x 107 1. Make exponents the same 2. Subtract 2.0 - .063 and keep the 107

Multiplying To multiply numbers in scientific notation: Step 1 : Group the numbers together. Step 2 : Multiply the numbers. Step 3 : Add the powers of 10. Step 4 : Give the answer in scientific notation.

3x108 x 1.5x1023 = Step 1 : Group the numbers together. Step 2 : Multiply the numbers. Step 3 : Add the powers of 10. Step 4 : Give the answer in scientific notation. (3x1.5)x(108+23) =4.5x1031 4.0x108 x 5.0x106 = (4.0x5.0) x 108+6 = 20x1014 =2.0x1015

Dividing To divide numbers in scientific notation: Step 1 : Group the numbers together. Step 2 : Divide the numbers. Step 3 : Subtract the powers of 10. Step 4 : Give the answer in scientific notation.

4.5x108 3x105 4.5 3 x 108-5 Step 1 : Group the numbers together. Step 2 : Divide the numbers. Step 3 : Subtract the powers of 10. Step 4 : Give the answer in scientific notation. = 1.5x103

Practice makes perfect! So let’s practice!