Standard Form to Scientific Notation Day 41 Learning Target: Students can convert numbers from standard form into scientific notation.

What is scientific Notation? Scientific notation is a way of expressing really big numbers or really small numbers. It is most often used in “scientific” calculations where the analysis must be very precise.

Why use scientific notation? For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form. Numbers expressed in scientific notation can be used in a computation with far greater ease.

Let’s compare the two… SCIENTIFIC NOTATION STANDARD FORM 9,200,000,000,000,000 .0000000000254 -23,000,000,000 -.000091 9.2 x 1015 2.54 x 10-11 -2.3 x 1010 -9.1 x 10-5

An ordinary quarter contains about 97,700,000,000,000,000,000,000 atoms. The average size of an atom is about 0.00000003 centimeters across. These very long numbers are written in **STANDARD FORM** **The length of these numbers in standard notation makes them awkward to work with. What is in the pink boxes is what goes in any of the blanks on the Know-It Notes Scientific notation is a shorthand way of writing numbers – instead of standard notation.

Standard Form Scientific Notation 82,000,000 Find a number bigger than 1, less than 10 Only 2 decimal places This is your NEW decimal Multiply by 10 ( x 10) 3. Count decimal spaces from NEW to OLD (this is your exponent on 10) 4. LEFT = NEGATIVE RIGHT = POSITIVE (exponent) 1. 8.2 2. 8.2 x 10 3. 7 Spaces (8.2 x 107) 4. Right

In scientific notation the number of atoms in a quarter (97,700,000,000,000,000,000,000 ) is 9.77  1022 and the size of each atom (0.00000003) is 3.0  10–8 centimeters across.

Write 0.00709 in scientific notation. Example 1: Write 0.00709 in scientific notation. 0.00709 Move the decimal to get a number between 1 and 10. (*you want only one number behind the decimal) 7.09  10 Set up in scientific notation. Think: The decimal needs to move left to change 7.09 to 0.00709, so the exponent will be negative. Think: The decimal needs to move 3 places 0.00709 written in scientific notation is 7.09  10–3. Check 7.09  10–3 = 7.09  0.001 = 0.00709

K H D M D C M Example 2: 1 cm = 10 mm 18.7 cm = 187 mm Multiply by 10 A pencil is 18.7 cm long. If you were to lay 10,000 pencils end-to-end, how many millimeters long would they be? Write the answer in scientific notation. Hint: Convert from cm to mm Find the length of 10,000 pencils K H D M D C M 1 cm = 10 mm 18.7 cm = 187 mm Multiply by 10 Find the total length. 187 mm  10,000 Multiply 1,870,000 mm

Set up scientific notation. Example 3 continued: 1,870,000 mm Set up scientific notation. In scientific notation the 10,000 pencils would be 1.87  106 mm long, laid end-to-end.

Remember… If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

Example 4 Given: 289,800,000 Use: 2.898 (moved 8 places) Answer: 2.898 x 108

Example 5 Given: 0.000567 Use: 5.67 (moved 4 places) Answer: 5.67 x 10-4