Physical Quantities

Physical Quantities

We define a physical quantity by how it is measured or by how it was calculated from measured values. For example, the mass of an object in grams is a physical quantity because it is measured using a scale. The speed of a moving object in meters per second is also a physical quantity because it is based on two measured quantities (distance in meters, and time in seconds).

SI units are standardized units of measure for different measured quantities. The fundamental SI units are the following:

Derived SI units are based on the fundamental SI units. An example is speed, which is length per unit time.

Prefixes

SI units are part of the metric system. The metric system is convenient for scientific and engineering calculations because the units are categorized by factors of 10. The table below gives metric prefixes and symbols used to denote various factors of 10.

Conversion of units and Dimensional analysis

Unit conversion is to express the value of a given quantity in different units using a conversion factor.

 In order to complete the conversion process we use dimensional analysis.

The analysis can be done using the following equation:

Significant Figures:

Using the method of significant figures, the rule is that the last digit written down in a measurement is the first digit with some uncertainty. In order to determine the number of significant digits in a value, start with the first measured value at the left and count the number of digits through the last digit written on the right. For example, the measured value 24.7cm has three digits, or significant figures.

Significant figures indicate the precision of a measuring tool that was used to measure a value.

Rules for significant figures:

1. Non-zero digits are always significant;275 has four significant digits.
2. Any zeros between two significant digits are significant; 1.08701 has six significant digits.
3. Zeros before the decimal point are placeholders and not significant; in the number .00371, only the 3,7 and 1 are significant, meaning the number has 3 significant figures.
4. Zeros after the decimal point and after figures are significant; in the number 0.2540, the 2, 4, 5 and last 0 are significant.
5. Exponential digits in scientific notation are not significant; 12x10⁶has three significant digits, 1, 1, and 2.

These rules ensure accurate representation and interpretation of data. If, for example, you were to read of an experimental reaction in which the resulting chemical weighed 0.0254 g, you would know that the measurement is accurate to 0.0001 g and contains 3 significant figures.

Determine the number of significant figures in the following measurements:

1. 0.0009
2. 15,450.0
3. 6×10³
4. 87.990
5. 30.42

Solution

(a) 1; the zeros in this number are place holders that indicate the decimal point

(b) 6; here, the zeros indicate that a measurement was made to the 0.1 decimal point, so the zeros are significant

(c) 1; the value 10³ signifies the decimal place, not the number of measured values

(d) 5; the final zero indicates that a measurement was made to the 0.001 decimal point, so it is significant

(e) 4; any zeros located in between significant figures in a number are also significant