Very large numbers with many zeros, such as1,000,000,000,000,000, or very small numbers,such as 0.0000000000000001, are very cumber-some to work with. Consequently, the numbersare expressed in a kind of mathematical short-hand known as scientific notation. Scientificnotation has the following form:

M × 10 n

where n specifies how many times the number M is raised to the power of 10. The exponent n hastwo meanings, depending on its sign. If n is posi-tive, M is multiplied by 10 n times. For example,if n = 2 and M = 1.2, then

1.2 × 10 2 = 1.2 × 10 × 10 = 120

In other words, if n is positive, the decimal pointof M is moved to the right n times. In this case

the decimal point of 1.2 is moved two places tothe right.

1.20.

If n is negative, M is divided by 10 n times.

1.2 × 10 – 2 =

1.2

(10 × 10)

=

1.2

(100)

= 0.012

Two common examples of the use of scien-tific notation in chemistry are Avogadro’s numberand pH. Avogadro’s number, 6.023 × 10 23 , is thenumber of atoms in 1 molar mass of an element.Thus

6.023 × 10 23 = 602,300,000,000,000,000,000,000

which is a very large number of atoms.The pH scale is a measure of the concentrationof hydrogen ions in a solution. A neutral solutionhas 10 – 7 moles of hydrogen ions per liter. Inother words

10 – 7 = 0.0000001

which is a very small amount (1 ten-millionth ofa gram) of hydrogen ions.

In other words, if n is negative, the decimal pointof M is moved to the left n times. In this case,the decimal point of 1.2 is moved two places tothe left.

0.01.2

If M is the number 1.0, it often is not expressedin scientific notation. For example, 1.0 × 10 2 isthe same thing as 10 2 , and 1.0 × 10 – 2 is the samething as 10 – 2 .

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