Standard Form to Scientific Notation Day 41 Learning

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

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

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

Let’s compare the two… STANDARD FORM 9, 200, 000, 000 n. 00000254 n -23, 000, 000 n -. 000091 n SCIENTIFIC NOTATION 9. 2 x 1015 n 2. 54 x 10 -11 n -2. 3 x 1010 n -9. 1 x 10 -5 n

1. An ordinary quarter contains about 97, 700, 000, 000 atoms. 2. 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. Scientific notation is a shorthand way of writing numbers – instead of standard notation.

Standard Form Scientific Notation 82, 000 1. Find a number bigger than 1, less than 10 1. 8. 2 Multiply by 10 ( x 10) 2. 8. 2 x 10 a. Only 2 decimal places b. This is your NEW decimal 2. 3. Count decimal spaces from NEW to OLD (this is your exponent on 10) 4. LEFT = NEGATIVE RIGHT = POSITIVE (exponent) 3. 7 Spaces (8. 2 x 107) 4. Right

In scientific notation the number of atoms in a quarter (97, 700, 000, 000 ) is 9. 77 1022 and the size of each atom (0. 00000003) 0. 00000003 is 3. 0 10– 8 centimeters across.

Example 1: Write 0. 00709 in scientific notation. 0. 00709 Move the decimal to get a number between 1 and 10. 7. 09 10 (*you want only one number behind the decimal) 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

Example 2: 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: K H D M D C M 1. Convert from cm to mm 2. Find the length of 10, 000 pencils 1 cm = 10 mm 18. 7 cm = 187 mm 10, 000 1, 870, 000 mm Multiply by 10 Find the total length. Multiply

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… n 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 n Given: 289, 800, 000 n Use: 2. 898 (moved 8 places) n Answer: 2. 898 x 108

Example 5 n Given: 0. 000567 n Use: 5. 67 (moved 4 places) n Answer: 5. 67 x 10 -4