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2.1 Exponents and Scientific Notation Did you ever take a shortcut when walking from one place to another? You can also use shortcuts in math. When you use an exponent, you are writing a long multiplication problem in a shortened form. An ___________________________ tells you how many times to use the base number as a factor in a multiplication problem. There are two parts to a number written in exponential form: 35 exponent Base number This tells you to use the base number, 3, as a factor 5 times = 3 x 3 x 3 x 3 x 3 = _________ The zero (0) power of any number is always _________. The first power (1) of any number is that number. Prime Factorization 200 Find the prime factorization of 200, in exponent form: 1) Make a factor tree and factor the number until you have all prime numbers: _______________ 2) Write the factorization in exponent form: ________ Scientific Notation On average, the Earth is 92,900,000 miles from the sun. It is convenient to write very large numbers in a shortened form, called ____________ ________________. Scientific notation expresses a number as the product of a decimal number from 1-9 and a power of 10. To write numbers in scientific notation: 1) Remove all the zeroes from the end of the number: 92,900,000. 2) Write the remaining digits as a decimal number from 1-9: 9.29 3) Count the number of decimal places you moved back. This will be your power of ten. 92,900,000. 4) Scientific notation of 92,900,000: _____________________ Write in scientific notation. 88,900 809,123 Challenge: 340.0200 To write a scientific number in standard form: 1) move the decimal point forward the same number of spaces as the exponent 2) 2.34 x 107 = move the decimal point forward 7 spaces and write the new number. Answer: ____________ 3) 2.34 x 10-7 = move the decimal point backward 7 spaces and write the new number. _______________ Write in standard form. 1.092 x 104 6 x 10-8 Challenge: 5.6554 x 103