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Principles of Chemistry Online

Lecture Notes

Introductory Chemistry, 2nd ed, by Nivaldo Tro Chapter 02: Measurements and Problem-Solving Part 1: Measurements

Measurement of Matter: the Metric System

All measurements consists of two parts: a number and unit. Keeping the number and the units together is  very important. A number without an accompanying unit is meaningless.  Always (!!) write out the units for the numbers you use in calculations and problem-solving. The cool thing about units is that you can do the same algebraic operations with units that you do with numbers and in this course, you will learn a method of problem-solving in which the units of the numbers will help lead you to the correct calculation.

Scientific Notation

Scientific notation is a way of expressing very large or very small numbers in terms of powers of ten, written as a number with a value between 1 and 10 (called the coefficient) which is multiplied by a power of 10 (called the exponent. ) For example, in the number 1.7 x 109,  the exponent “9” tells us that the decimal point was moved nine places to the left from where it started in the original number.  Therefore the actual number is 1,700,000,000, a very large number.  Thus large numbers will have a positive exponent while very small numbers will have negative exponent.  In the example 5.6 x 10-6, the exponent “–6” tells us that the decimal place was moved 6 places to the right from its place in the original number, so the regular number is 0.0000056.  Practice converting numbers to scientific notation and vice versa.  Study the examples in the chapter and in the powerpoint slides.

Using Scientific Notation on Your calculator.

Practice entering and doing calculations using scientific notation on your calculator.  Most scientific calculators have a button named either “EE” or “exp” for entering exponents. Two common types of calculators used by students include the TI-83 or TI-84 series and the TI-30 series. Numbers in scientific notation are entered in a slightly different manner for these two types of calculator.

When using a TI-83 and trying to enter scientific notation, do not enter the "10" before the exponent or you will not get the correct answer. Often, when a student’s answer is off by a factor of ten, this is the detail that causes the answer to be off. Scientific Notation on a TI-83 or TI-84

To enter a number  such as 1.7 x 10 -9 in scientific notation in the TI-83 calculator, enter “1.7”, then the yellow "2nd" button to shift, then the comma button (this gives the "EE" function because we previously hit "2nd") followed by the exponent. If the exponent is negative, push the (-) button (located in the bottom row of buttons next to the decimal point) before you enter the number for the exponent.  Do not enter the "10" before you enter the exponent: the “EE” function takes the place of “times ten to the.” To recap: To enter 1.7 x 10 -9 in a TI-83 calculator, enter 1.7, "2nd", "EE", (-)9 and then push the enter button and continue on with your calculation.

Scientific Notation on a TI-30XA

There are several different models of TI-30XA calculators that look a little different from each other. It appears that  TI-30XA calculators all have an "EE" button, so you will not need to use the "2nd" function to use the "EE". Do not enter the "10" if you are using the "EE" button. Simply type in the coefficient, hit the EE button, then type the exponent. If it is a negative exponent, you should hit the change sign button (on the bottom row just to to left of the equals sign ) before you type in the number for the exponent.

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