Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
STANDARD FORM 9,200,000,000,000,000 .0000000000254 -23,000,000,000 -.000091 SCIENTIFIC NOTATION 9.2 x 1015 2.54 x 10-11 -2.3 x 1010 -9.1 x 10-5 1. An ordinary quarter contains about 97,700,000,000,000,000,000,000 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. 82,000,000 1. Find a number bigger than 1, less than 10 a. b. 2. Only 2 decimal places This is your NEW decimal 1. 8.2 2. 8.2 x 10 3. 7 Spaces (8.2 x 107) 4. LEFT Multiply by 10 ( x 10) 3. Count decimal spaces from NEW to OLD (this is your exponent on 10) 4. LEFT = POSITIVE RIGHT = NEGATIVE (exponent) 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. Example 2: 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 So 0.00709 written in scientific notation is 7.09 10–3Check . 7.09 10–3 = 7.09 0.001 = 0.00709 Example 3: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 Hint: notation. 1. Convert from cm to mm 2. Find the length of 10,000 pencils 1 cm = 10 mm 18.7 cm = 187 mm 187 mm 10,000 1,870,000 mm KHDMDC M Multiply each side by 10 Find the total length. Multipl y Example 3 continued: 1.87 106 Set up scientific notation. Think: The decimal needs to move right to change 1.87 to 1,870,000, so the exponent will be positive. Think: The decimal needs to move 6 places. In scientific notation the 10,000 pencils would be 1.87 106 mm long, laid end-to-end. (5.23 X 107) The exponent on the 10 tells you how many spaces you will move the decimal If the exponent is POSITIVE move RIGHT If the exponent is NEGATIVE move LEFT EXAMPLES: 3.75 x 109 = 3,750,000,000 8.62 x 10-6 = .00000862 Example 1: Write the number in standard notation: A. 1.35 105 BECAUSE 1.35 105 1.35 100,000 135,000 105 = 100,000 Think: Move the decimal right 5 places. Helpful Hint A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the Example Write the number in standard notation: 1: HINT: –3 B. 2.7 10 Just remember that since the exponent is negative we move the decimal to the left 3 spaces 2.7 10–3 1 2.7 10x10x10 10 -3 2.7 1000 0.0027 1 = 1000 Divid by the reciprocal. e Think: Move the decimal left 3 places. Example Write the number in standard notation: 1: C. -2.01 HINT: It doesn’t matter that the number (104 -2.01 104 2.01) is negative – only the exponent changes things -2.01 104 = 10,000 -20,100 10,000 Think: Move the decimal right 4 places. **Because 4 is POSITIVE** Quiz: Write each number in standard notation. 1. 1.72 104 17,200 2. 6.9 10–3 0.0069 Write each number in scientific notation. 3. 0.0053 5.3 10–3 4. 57,000,000 5.7 107 5. Order the numbers from least to greatest: 2 10–4 , 9 10–5 , 7 10–5 7 10–5, 9 10–5, 2 10–4