![]() ![]() The purpose of this chapter is to introduce you to some of the terminology and mathematical notation used in chemistry. Įvery academic discipline has its own jargon. For numbers less than 1, the exponent is a negative whole number that indicates the number of times the coefficient must be divided by 10 (or multiplied by 0.1) to give the number represented in scientific notation ĭo not use X 10 when entering exponential numbers on a calculator this multiplies your answer by 10. We can, for example, write įor numbers larger than 1, the exponent in scientific notation is a positive whole number, as illustrated above. The second is that it removes the ambiguity in the number of significant figures in a number ending with zeroes. The first, as illustrated in Table B.l, is that the very large and very small numbers often dealt with in the sciences are much less cumbersome in scientific notation. There are two great advantages to scientific notation. The exponent indicates the number of lO s hy which the coefficient is multiplied to give the number represented in scientific notation The second term, the exponential term, is 10 raised to a power-the exponent. The first term, the coefficient, is a number between 1 and 10. Scientific notation, also known as exponential notation, is a way of representing large and small numbers as the product of two terms. So in scientific notation this is given as 4.39 x 10. To give the original answer we need to multiply by 0.000001 or 10. The appropriate number between 1 and 10 is 4.39. So in scientific notation we write this as 8.352 x 10. This number needs to be multiplied by 1000 or 10 to give the original value. First we need to write the appropriate number between 1 and 10, which is 8.352. It follows from the above that the number written as For example, 10 = 1/10, as shown in Chapter 1. This is true of any number expressed in scientific notation. ![]() The common feature of these values is that they consist of a number between 1 and 10 multiplied by a power of 10. Examples include a wavelength of 1.54 x 10 ° m and the value of Planck s constant 6.63 X10 J s. Scientific notation is frequently used in chemistry where we encounter both very small and very large quantities. By the way, did you notice you can easily solve this problem without a calculator Try regrouping the mantissas separately from the powers of 10. The division bar is a symbol of enclosure, so do the operations in the numerator and in the denominator before performing the division. Remember to follow the rules for symbols of enclosure. ![]() Unfortunately, these calculators also have a 10 key, which is the antilog key and has nothing to do with scientific notation, so don t use it when entering numbers in scientific Calculators vary widely, but virtually all scientific calculators have either an EE key or an EXP key that is used for scientific notation. It is critical that you learn to use the scientific notation feature of your calculator properly. You will probably use your calculator for most calculations. So, if you DECREASE 12.5 to 1.25, wouldn t you need to INCREASE the exponent to cancel out this change So, the correct answer is 1.25 x 10-2. You want your answer to be equal to the initial number. Can you convert 12.5 x 10 3 into proper form You have to move the decimal point one place to the left, but does the exponent increase or decrease Is the correct answer 1.25 x 10-4 or 1.25 x 10-2 Rather than memorize a rule, think of it this way. Numbers in proper scientific notation have only one digit in front of the decimal place. The order of magnitude is expressed as a power of 10, and indicates how many places you had to move the decimal point so that only one digit remains to the left of the decimal point. In scientific notation, only one digit in the mantissa is to the left of the decimal place. A number in scientific notation consists of a number multiplied by a power of 10. Scientific notation uses exponents (powers of 10) for handling very large or very small numbers. ![]()
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