Smaller vs. Larger Exponents and NumbersDate: 03/24/2003 at 12:54:07 From: Toni Subject: Numbers and exponents Is a smaller number with a large exponent greater than a larger number with a smaller exponent? Using the numbers 1,2,3,4 what is the largest number you could make? I'm thinking of 2^431 or 21^43. Date: 03/25/2003 at 15:10:36 From: Doctor Ian Subject: Re: Numbers and exponents Hi Toni, Generally, it's big exponents that give you power. Compare 99 2 to 2 99 However, the 'logic' you use to answer a question like this involves understanding how exponents work, which is explained here: Properties of Exponents http://mathforum.org/library/drmath/view/57293.html So before reading on, make sure you understand the basic rules. Ready? To compare numbers like 431 43 2 ? 21 one thing you can do is try to get similar exponents. For example, 431 10 43 2 = 2 * (2 ) 43 = 2 * (1024) Now, 1024 raised to the 43rd power is going to be a _lot_ bigger than 21 raised to the same power, right? Another way to do the comparison is to try to get close to powers of 10. For example, since 2^10 is close to 1000, we can approximate 431 10 43 ('~' means 'approximately equals') 2 ~ (2 ) 3 43 ~ (10 ) 129 ~ 10 Let's see what happens with 21^43: 43 43 21 ~ (2*10) 43 43 ~ 2 * 10 Now we can use the same trick. 10 4 43 ~ (2 ) * 10 3 4 43 ~ (10 ) * 10 12 43 ~ 10 * 10 55 ~ 10 I hope this helps. Write back if you'd like to talk more about this, or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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