Scientific NotationDate: 08/19/97 at 03:27:49 From: Anthony Raciti Subject: Scientific notation Write these numbers in scientific notation: (a) 55000 (b) 250 000 (c) x (d) 0.55 (e) 0.000 25 (f) 0.000 000 000 08 Date: 08/25/97 at 12:15:48 From: Doctor Rob Subject: Re: Scientific notation Writing numbers in scientific notation is to put them in the form a*10^b, where 1 <= a < 10 and b is an integer. Moving from left to right through the digits of the number, find the first one which is nonzero. Copy it and all the following digits. Put a decimal point after this digit. Truncate trailing zeroes. Now figure out what power of 10 you have to multiply by this to get the original number. This is the same as the number of digits the decimal point has moved, with a + sign if it moved to the left and a - sign if it moved to the right. Example: (a) The first nonzero digit is the leftmost 5. Copy down the digits 55000 . Put the decimal place after the leftmost 5: 5.5000 . Truncate the trailing zeroes to get 5.5 . Since the decimal point has moved 4 places to the left, the power of 10 is +4, and the answer is 5.5*10^4 . Note: (c) is a trick. Since you don't have any idea what size x is, it can't be written in scientific notation. You can do the rest. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 08/20/97 at 18:17:06 From: Doctor Barney Subject: Re: scientific notation In science, we often deal with very large or very small numbers. Numbers like 900,000,000 or 0.0000003. When numbers are written in this form, they can be very difficult to manipulate. For example, how would you multiply the two numbers I just gave you? In scientific notation, we write the number as the product of two different parts. The first part is a number between one and ten, like 5.5 or 2.5. Numbers between one and ten are usually pretty easy to manipulate. The second part is a power of ten. That just means 10 or 100 or 1000 or 100,000,000,000 or 0.01 or 0.00001, but instead of writing all those zeros, we write it as an exponent. For example, 100 = 10^2 (ten squared) 100,000 = 10^5 (ten to the fifth power) 0.001 = 10^-3 (ten to the minus three) Every rational number can be written as the product of a number between one and ten, and a power of ten. For example, 900,000,000 = 9x10^8 0.0000003 = 3x10^-7 These numbers are very easy to multiply because 9x3 = 27 and 10^8 x 10^-7 = 10 (remember that when you multiply two numbers with the same base you can just add the exponents). The final answer is 27x10 = 270. There is a shortcut you can use if you want to. Move the decimal point to the right or to the left until you have a number between one and ten. Count the number of places you had to move the decimal point and that number is the exponent in your scientific notation, except that the exponent will be negative if you had to move the decimal point to the right. For example, to get from 900,000,000 to 9, I had to move the decimal point 8 places to the left. To get from 0.0000003 to 3 I had to move the decimal point 7 places to the right -Doctor Barney, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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