Chemistry Workbook For Dummies
Understanding introductory chemistry is critical for your success in all science classes to follow; keeping up with the material now makes life much easier down the education road. Chemistry Workbook For Dummies gives you the practice you need to succeed! Christopher Hren is a high school chemistry teacher and former track and football coach. Peter J. Mikulecky, PhD, teaches biology and chemistry at Fusion Learning Center and Fusion Academy.
Chemistry Workbook For Dummies
Noting Numbers Scientifically
IN THIS CHAPTER
Crunching numbers in scientific and exponential notation
Telling the difference between accuracy and precision
Doing math with significant figures
Like any other kind of scientist, a chemist tests hypotheses by doing experiments. Better tests require more reliable measurements, and better measurements are those that have more accuracy and precision. This explains why chemists get so giggly and twitchy about high-tech instruments: Those instruments take better measurements!
How do chemists report their precious measurements? What's the difference between accuracy and precision? And how do chemists do math with measurements? These questions may not keep you awake at night, but knowing the answers to them will keep you from making rookie mistakes in chemistry.
Using Exponential and Scientific Notation to Report Measurements
Because chemistry concerns itself with ridiculously tiny things like atoms and molecules, chemists often find themselves dealing with extraordinarily small or extraordinarily large numbers. Numbers describing the distance between two atoms joined by a bond, for example, run in the ten-billionths of a meter. Numbers describing how many water molecules populate a drop of water run into the trillions of trillions.
To make working with such extreme numbers easier, chemists turn to scientific notation, which is a special kind of exponential notation. Exponential notation simply means writing a number in a way that includes exponents. In scientific notation, every number is written as the product of two numbers, a coefficient and a power of 10. In plain old exponential notation, a coefficient can be any value of a number multiplied by a power with a base of 10 (such as 104). But scientists have rules for coefficients in scientific notation. In scientific notation, the coefficient is always at least 1 and always less than 10. For example, the coefficient could be 7, 3.48, or 6.0001.
To convert a very large or very small number to scientific notation, move the decimal point so it falls between the first and second digits. Count how many places you moved the decimal point to the right or left, and that's the power of 10. If you moved the decimal point to the left, the exponent on the 10 is positive; to the right, it's negative. (Here's another easy way to remember the sign on the exponent: If the initial number value is greater than 1, the exponent will be positive; if the initial number value is between 0 and 1, the exponent will be negative.)
To convert a number written in scientific notation back into decimal form, just multiply the coefficient by the accompanying power of 10.
Q. Convert 47,000 to scientific notation.
A. . First, imagine the number as a decimal:
Next, move the decimal point so it comes between the first two digits:
Then count how many places to the left you moved the decimal (four, in this case) and write that as a power of 10: .
Q. Convert 0.007345 to scientific notation.
A. . First, put the decimal point between the first two nonzero digits:
Then count how many places to the right you moved the decimal (three, in this case) and write that as a power of 10: .
1 Convert 200,000 into scientific notation.
2 Convert 80,736 into scientific notation.
3 Convert 0.00002 into scientific notation.
4 Convert from scientific notation into decimal form.
Multiplying and Dividing in Scientific Notation
A major benefit of presenting numbers in scientific notation is that it simplifies common arithmetic operations. The simplifying abilities of scientific notation are most evident in multiplication and division. (As we note in the n