Measurements scientific notation

Having surveyed some of the units used in chemistry, we now turn to techniques for handling numbers associated with measurements scientific notation and significant figures. 

Chemists frequently work with measurements that are very large or very small. A mole, for example, contains 602,213,670,000,000,000,000,000 particles, and some analytical techniques can detect as little as 0.000000000000001 g of a compound. For simplicity, we express these measurements using scientific notation thus, a mole contains 6.0221367 X 10 particles, and the stated mass is 1 X 10 g. Sometimes it is preferable to express measurements without the exponential term, replacing it with a prefix. A mass of 1 X 10 g is the same as 1 femtogram. Table 2.3 lists other common prefixes. 

In general, any ambiguity concerning the number of significant figures in a measurement can be resolved by using exponential notation (often referred to as scientific notation ), discussed in Appendix 3. 

As usual, Feynman was right. His little particles captures an essential fact about atoms. They are tiny—so tiny that a teaspoon of water contains about 500,000,000,000,000,000,000,000 of them. Handling numbers this big is awkward. Try dividing it by 63, for example. To accommodate the very large numbers encountered in counting atoms and the very small ones needed to measure them, chemists use the scientific notation system. 

Any zero to the right of nonzero digits and to the left of a decimal point and not covered by rule 2 may or may not be significant, depending on whether the zero is a placeholder or actually part of the measurement Such a number should be expressed in scientific notation to avoid any confusion. 

Usin0 Exponential and Scientific Notation to Report Measurements... 

When you know how to express your numbers in scientific notation and how to distinguish between precision and accuracy (we cover both topics earlier in this chapter), you can bask in the glory of a new skill using scientific notation to express precision. The beauty of this system is that simply by looking at a measurement, you know just how precise that measurement is. 

Be a good chemist. Report your measurements in scientific notation to avoid such annoying ambiguities. (See the earlier section Using Exponential and Scientific Notation to Report Measurements for details on scientific notation.)... 

Chemists routinely measure quantities that run the gamut from very small (the size of an atom, for example) to extremely large (such as the number of particles in one mole). Nobody, not even chemists, likes dealing with scientific notation (which we cover in Chapter 1) if they don t have to. For these reasons, chemists often use a metric system prefix (a word part that goes in front of the base unit to indicate a numerical value) in lieu of scientific notation. For example, the size of the nucleus of an atom is roughly 1 nanometer across, which is a nicer way of saying 1x10- meters across. The most useful of these prefixes are in Table 2-2. 

Your lab partner has measured the mass of your sample to be 2,500 g. How can you record this more nicely (without scientific notation) in your lab notebook using a metric system prefix ... 

The conventional representation of numbers using scientific notation is not always followed. For example, we might represent a bond length as 0.14x 10-9 m rather than 1.4 x 10-10 m if we were referencing it to another measurement of length given in integer unit multiples of 10 9 m. 

Convert the following measurements from scientific notation to standard notation ... 

A couple of comments are in order here. First, did you notice the value of the pH is the same as the absolute value of the exponent This will always be true when the first part of the scientific notation is exactly 1. The second comment relates to significant figures. There are two significant figures in the molarity measurement of 1.0 x 10 3 M. There are also two significant figures in the pH value of 3.00. Finally, pH values have no intrinsic units. Logarithms represent pure numbers, and as such, have no units. 

Mole A mole is a measure of amount of substance. One mole is the formula weight of the substance expressed in grams. For example, for limonene, formula C10H16, the formula weight is (C = 12) (10 x 12) + (16 x 1) (H = 1) = 136 so that one mole of limonene is 136 grams of the compound. One mole of any substance contains the same number of units (atoms, molecules or ions). This is termed the Avogadro number, 6.022 x 1023 in scientific notation. 

What if you were able to measure the volume of water in the Great Lakes You could verify the value of 22 700 km3. Then all five digits (including the zeros) would be significant. Here again, scientific notation lets you show clearly the five significant digits 2.2700 x 104 km3. 

When adding or subtracting numbers in scientific notation, the numbers must be converted to the same power of 10 as the measurement with the greatest power of 10. Once the numbers are all expressed to the same power of 10, the power of 10 is neither added nor subtracted in the calculation. 

For very large numbers with units of measure, use scientific notation or choose an appropriate multiplying prefix for the unit to avoid numbers of more than four digits. 

The viscosity of carbon dioxide at 575.15 K has been measured as 0.0002682 p. In scientific notation we would write this as 2.682 p, realising that we need to include a factor of 0.0001 or 10 to correctly scale this. The value could thus be quoted as 2.682 x 10 " p. 

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