# Dimensional Analysis

How would you like have to calculate with: 1 mol 602,200,000,000,000,000,000,000 atomsor 1 Dalton 0.000,000,000,000,000,000,000,00165 g You can streamline large or small numbers with scientific notation. The standard is that you place the decimal point after the first significant digit and adjust the exponent of ten so that there is no change in the value of the number.
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Then you must do the opposite (inverse) to the exponent part of the new expression so that there is no change in the value of the number. (0.000,000,000,000,000,000,000,00165 x 10 24 ) x 1/.65 x or 1.65 E - 24 (602,200,000,000,000,000,000,000/ 10 23 ) x.022 x or 6.022 E23 The original numbers have the same value as the exponential forms.
Don't get caught making too much of this. You have seen it before. The number "five point two million" is the same as 5.2 E6. The number of the power of ten only indicates how many places you need to move the decimal to get the long form of the number back.
Think of the change as creating a new number with two parts, a digit part and an exponent part, from the old number. To put the decimal point behind the first digit, you must divide or multiply the original number by some integer power of ten.
Measured numbers are an estimated amount, measured to a certain number of significant figures without the benefit of any natural unit or numbers that come from a mathematical operation such as averaging.
Full number Words for number Sci. Notation styles 5,000,000,000 five billion (USA) 5.0 x 10 9 or 5.0 E9 500,000,000 five hundred million 5.0 x 10 8 or 5.0 E8 50,000,000 fifty million 5.0 x 10 7 or 5.0 E7 5,000,000 five million 5.0 x 10 6 or 5.0 E6 500,000 five hundred thousand 5.0 x 10 5 or 5.0 E5 50,000 fifty thousand 5.0 x 10 4 or 5.0 E4 5,000 five thousand 5.0 x 10 3 or 5.0 E3 500 five hundred 5.0 x 10 2 or 5.0 E2 50 fifty 5.0 x 10 1 or 5.0 E1 5 five 5.0 x 10
Back to the beginning of Numbers and Math. Operations. Measured vs. Exact numbers, exact numbers are numbers that are exact by definition, such as: 1 inch 2.54 cm or 1 gallon 231 cubic inches or 1 foot 12 inches or 1 meter 100 centimeters or numbers that come in integers and are not likely to be available in amounts smaller.