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Scientific Notation What is it again? • • • It is where we represent very BIG or very SMALL numbers with 10x where we multiply them with a rounded power of 10 4 x 103 = _________________________ 5.32 x 10-4 = __________________________________ How to punch into a calculator? • • On your calculator, you have multiple buttons – EXP – EE – Or manually punching in x 10 x To put an exponent, you have multiple buttons too –Y –X –^ x • y Try punching in 3.1 x 104 into your calculator How to multiply and divide with sci. notation? • • • Multiply the first value with the first value of each sci. notation Multiply the base 10’s like you would with exponent laws. (REVIEW THIS) 102 x 103 = ___________________________________- • • • • • 2.3 x 102 x 3.44 x 103 You have to multiply 2.3 x 3.44 Then multiply the 102 and the 103 and you will get ______________ Or you can punch it all into your calculator as (2.3 x 102) x (3.44 x 103) Example - 1 • (7.89 x 103) x (9.65 x 105) • (8.65 x 104) ÷ (5.455 x 102) Adding and Subtracting Sci. Notation • • • • • You must make the exponents of the base 10 the same! 2 x 102 + 1 x 103 , you must convert either one to the other exponent 0.2 x 103 + 1 x 103 = _____________________ 2 x 102 + 10 x 102 = ___________________________ Or you can punch it into your calculator Example - 2 • • 5.6 x 103 + 4.43 x 102 4.545 x 102 – 1.3434 x 102 Decimal Rules for Exponents • • • • • • • • Move decimal left = exponent gets ________________ 23.4 x 103 Move decimal left 1 position and the 3 turns into a 4 _____________________ Move decimal right = exponent gets _________________ 2.34 x 104 Move decimal right 1 position, the 4 turns back into a 3 ____________________ Scientific notation to Standard Notation • You want your 10x to turn into 100 because anything to the exponent of 0 is equal to 1. • • • • • • • • • • • You look at the exponent for the 10x This is the number of ZEROES _______________________________________________________ 8 x 104 means you are adding 4 zeroes after 8 so it turns into _____ If the exponent is __________________ You are looking at adding that many zeroes before your value. So it becomes 0.000…. 8 x 10-3 means you are adding 0.00 (3 zeroes) before the 8 so it becomes __________________ But, if there are already values after the decimal, those values COUNT as ZEROES! 9.4124 x 109, the 4124 counts as 4 zeroes, so you only have to add 5 more. =__________________ For negative exponents, since the decimals are already after the zeros, you just add them after your first digit. 9.4124 x 10-3 = ____________________ Standard to Scientific • • • Keep the first digit and __________________________ Put the rest of the NON-ZERO digit after the decimal Count the number of digits after the FIRST digit that you put a decimal in front. _________________________________________ • • • • • • 954353 turns into 9.54353 x 105 as there are 5 digits after the 9 If it is a decimal such as 0.009765. You have to put the first non-zero digit you see as your first value and then a decimal. Then put the rest of the digits after the decimal. 9.765 x 10x The exponent will be the number of zeroes before the 9. So in this case, you have 0.009 which is 3. So the exponent is -3. It is negative because the value is a decimal 9.765 x 10-3