Metric-USCS Conversions

Be wary of additions and subtractions. They sometimes increase or reduce the number of significant figures in an answer to greater or fewer than the number in any measured quantity. 

13 Given a metric-USCS conversion table and a quantity expressed in any unit in Table 3.3, express that quantity in corresponding units in the other system. 

The relationships between the number of metric units and the number of USCS units are direct proportionalities. You may find it useful to memorize only one conversion in each of three categories mass, length, and volume. You can then use familiar metric-metric and/or USCS-USCS conversions to change units within each system of measurement. Although it can add a few steps to a problem, this approach minimizes the amount of memorization necessary. 

In Table 3.3, notice two things about the length conversion 1 in. = 2.54 cm (1) The symbol for the USCS unit is in., including the period. The period distinguishes the unit symbol from the common word in. (2) The = symbol indicates a definition, and may be read one inch is defined as 2.54 centimeters. Thus exactly 1 in. is equal to exactly 2.54 cm, and the numbers are infinitely significant. There are other definitions in the table, also indicated by the = symbol. All other numbers are rounded, correct to the number of significant figures shown. 

The distances 54.00 in. and 4.500 ft are the same. They should be the same number of centimeters. But the answers to (a) and (b) are not the same. Make both calculations and explain the difference. 

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Table 3.3 Metric-USCS and USCS-USCS Conversion Factors...

Table 3.3 gives the more common conversion relationships between measurement units in the United States Customary System (USCS) and metric system. The USCS, formerly the British system of units, is the system used in the United States. All other countries of the world use the metric system. 

Chemistry problems often do not include all of the information necessary to find their solutions. It is typically assumed that you should either know or are able to look up information such as the density of a pure substance, as in this case, or a USCS-metric conversion, as in Section 3.6. In this hook, selected densities are given in Table 3.4. When you have what you need, Plan how you will solve the problem. You can choose dimensional analysis, algebra, or both for practice. We will show both solutions. Solve the remainder of the problem completely. 

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