Units of Measurement

The scientific community uses SI units for measurement of such properties as mass, length, and temperature. There are seven SI base units from which all other necessary units are derived.

 

 

 

 

 

 

 

 

 

The SI unit of temperature is the kelvin, although the Celsius scale is also commonly used. The Kelvin scale is known as the absolute temperature scale, with 0 K being the lowest theoretically attainable temperature.

K = ºC + 273.15

Figure 1.18 shows a comparison of the Kelvin, Celsius, and Fahrenheit scales.

Density has units of mass per unit volume and is often reported as grams per cubic centimeter, g/cm3.

Even the most carefully taken measurements are always inexact. This can be a consequence of inaccurately calibrated instruments, human error, or any number of other factors.

Two terms are used to describe the quality of measurements: precision and accuracy. Precision is a measure of how closely individual measurements agree with one another. Accuracy refers to how closely individually measured numbers agree with the correct or "true" value.

In order to convey the appropriate uncertainty in a reported number, we must report it to the correct number of significant figures. The number 83.4 has three digits. All three digits are significant. The 8 and the 3 are "certain digits" while the 4 is the "uncertain digit." As written, this number implies uncertainty of plus or minus 0.1, or error of 1 part in 834. Thus, measured quantities are generally reported in such a way that only the last digit is uncertain. All digits, including the uncertain one, are called significant figures.

Guidelines

  1. Nonzero digits are always significant–457 cm (3 significant figures); 2.5 g (2 significant figures).
  2. Zeros between nonzero digits are always significant–1005 kg (4 significant figures); 1.03 cm (3 significant figures).
  3. Zeros at the beginning of a number are never significant; they merely indicate the position of the decimal point–0.02 g (one significant figure); 0.0026 cm (2 significant figures).
  4. Zeros that fall at the end of a number or after the decimal point are always significant–0.0200 g (3 significant figures); 3.0 cm (2 significant figures).
  5. When a number ends in zeros but contains no decimal point, the zeros may or may not be significant–130 cm (2 or 3 significant figures); 10,300 g (3, 4, or 5 significant figures).

To avoid ambiguity with regard to the number of significant figures in a number with tailing zeros but no decimal point, such as 700, we use scientific (or exponential) notation to express the number. If we are reporting the number 700 to three significant figures, we can leave it written as it is, or we can express it as 7.00 102. There is no ambiguity in the latter regarding the number of significant figures, because zeros after a decimal point are always significant. However, if there really should be only two significant figures, we can express this number as 7.0 102. Likewise, if there should be only one significant figure, we can write 7 102. Scientific notation is convenient for expressing the appropriate number of significant figures. It is also useful to report extremely large and extremely small numbers. It would be most inconvenient for us to have to write all of the zeros in the number 1.91 10-24 (0.00000000000000000000000191).