Publisher Summary

Certain techniques in molecular biology, as in other disciplines of science, rely on types of instrumentation capable of providing precise measurements. An indication of the level of precision is given by the number of digits expressed in the instrument’s readout. The numerals of a measurement representing actual limits of precision are referred to as significant digits. This chapter discusses scientific notation and metric prefixes methods in expressing numbers. When expressing numbers in scientific notation, move the decimal point to the right of the leftmost nonzero digit, drop all zeros lying outside the string of significant figures, and express the new number as being multiplied by 10 having an exponent equal to the number of places the decimal point was moved from its original position (using a negative exponent if the decimal point was moved to the right). When adding or subtracting numbers expressed in scientific notation, rewrite the numbers such that they all have the same exponent value as that having the highest exponent, then perform the calculation. When multiplying numbers expressed in scientific notation, add the exponents. When dividing numbers expressed in scientific notation, subtract the exponent of the denominator from the exponent of the numerator to obtain the new exponent value. Numbers written in scientific notation can also be written using metric prefixes that will bring the value down to its lowest number of significant digits.

Introduction

There are some 3 000 000 000 base pairs (bp) making up human genomic DNA within a haploid cell. If that DNA is isolated from such a cell, it will weigh approximately 0.000 000 000 003 5 grams (g). To amplify a specific segment of that purified DNA using the polymerase chain reaction (PCR), 0.000 000 000 01 moles (M) of each of two primers can be added to a reaction that can produce, following some 30 cycles of the PCR, over 1 000 000 000 copies of the target gene.

On a day-to-day basis, molecular biologists work with extremes of numbers far outside the experience of conventional life. To allow them to more easily cope with calculations involving extraordinary values, two shorthand methods have been adopted that bring both enormous and infinitesimal quantities back into the realm of manageability. These methods use scientific notation and metric prefixes. They require the use of exponents and an understanding of significant digits.

1.1 Significant Digits

Certain techniques in molecular biology, as in other disciplines of science, rely on types of instrumentation capable of providing precise measurements. An indication of the level of precision is given by the number of digits expressed in the instrument’s readout. The numerals of a measurement representing actual limits of precision are referred to as significant digits.

Although a zero can be as legitimate a value as the integers one through nine, significant digits are usually nonzero numerals. Without information on how a measurement was made or on the precision of the instrument used to make it, zeros to the left of the decimal point trailing one or more nonzero numerals are assumed not to be significant. For example, in stating that the human genome is 3 000 000 000 bp in length, the only significant digit in the number is the 3. The nine zeros are not significant. Likewise, zeros to the right of the decimal point preceding a set of nonzero numerals are assumed not to be significant. If we determine that the DNA within a sperm cell weighs 0.000 000 000 003 5 g, only the 3 and the 5 are significant digits. The 11 zeros preceding these numerals are not significant.

1.2 Exponents and Scientific Notation

An exponent is a number written above and to the right of (and smaller than) another number (called the base) to indicate the power to which the base is to be raised. Exponents of base 10 are used in scientific notation to express very large or very small numbers in a shorthand form. For example, for the value 103, 10 is the base and 3 is the exponent. This means that 10 is multiplied by itself three times (103 = 10 × 10 × 10 = 1000). For numbers less than 1.0, a negative exponent is used to express values as a reciprocal of base 10. For example,