U Can: Chemistry I For Dummies. Hren Chris

example, the number expressed in scientific notation is 1.25 × 10^– 3 m. Most scientists express numbers in scientific notation.

      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.

       Tip: 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.

      In many cases, chemistry teachers refer to powers of 10 using scientific notation instead of their decimal form. With that in mind, here’s a quick chart showing you the most common powers of 10 used in chemistry along with their corresponding scientific notation.

       Examples

      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:

.

       Practice Questions

      1. Convert 200,000 to scientific notation.

      2. Convert 80,736 to scientific notation.

      3. Convert 0.00002 to scientific notation.

      4. Convert

from scientific notation to decimal form.

       Practice Answers

      1.

. Move the decimal point immediately after the 2 to create a coefficient between 1 and 10. Because you’re moving the decimal point five places to the left, multiply the coefficient, 2, by the power 10⁵.

      2.

. Move the decimal point immediately after the 8 to create a coefficient between 1 and 10. You’re moving the decimal point four places to the left, so multiply the coefficient, 8.0736, by the power 10⁴.

      2.

. Move the decimal point immediately after the 2 to create a coefficient between 1 and 10. You’re moving the decimal point five places to the right, so multiply the coefficient, 2, by the power 10^– 5.

      4. 690.3. You need to understand scientific notation to change the number back to regular decimal form. Because 10² equals 100, multiply the coefficient, 6.903, by 100. This moves the decimal point two places to the right.

      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 next section, addition and subtraction benefit from exponential notation but not necessarily from strict scientific notation.)

       Remember: To multiply two numbers written in scientific notation, multiply the coefficients and then add the exponents. To divide two numbers, simply divide the coefficients and then subtract the exponent of the denominator (the bottom number) from the exponent of the numerator (the top number).

       Examples

      Q. Multiply using the shortcuts of scientific notation:

.

      A.

. First, multiply the coefficients:

      Next, add the exponents of the powers of 10:

      Finally, join your new coefficient to your new power of 10:

      Q. Divide using the shortcuts of scientific notation:

.

      A.

. First, divide the coefficients:

      Next, subtract the exponent in the denominator from the exponent in the numerator:

      Then join your new coefficient to your new power of 10:

       Practice Questions

      1. Multiply

.

      2. Divide

.

      3. Using scientific notation, multiply

.

      4. Using scientific notation, divide

.

       Practice Answers

      1.

. First, multiply the coefficients:

. Then multiply the powers of 10 by adding the exponents:

. The raw calculation yields

, which converts to the given answer when you express it in scientific notation.

      2.

. The ease of math with scientific notation shines through in this problem. Dividing