Читать книгу U Can: Chemistry I For Dummies - Hren Chris - Страница 6

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. In exponential notation, a number is represented as a value raised to a power of 10. The decimal point can be located anywhere within the number as long as the power of 10 is correct.

Suppose that you have an object that’s 0.00125 meters in length. Express it in a variety of exponential forms:

All these forms are mathematically correct as numbers expressed in exponential notation. But in scientific notation the decimal point is placed so that only one digit other than zero is to the left of the decimal point. In the preceding 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:

Then count how many places to the right you moved the decimal (three, in this case) and write that as a power of 10: .

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.