Large and Small Numbers

Large and Small Numbers Expression, Units, and Prefixes... 

Logarithms are a convenient method for communicating large and small numbers. The logarithm, or log, of a number is the value of the exponent that 10 would have to be raised to, in order to equal this number. 

SCIENTIFIC NOTATION IS USED TO EXPRESS LARGE AND SMALL NUMBERS... 

To understand how this shorthand notation works, consider the large number 50,000,000. Mathematically this number is equal to 5 multiplied by 10 X 10X 10X 10X 10 X 10 X 10 (check this out on your calculator). We can abbreviate this chain of numbers by writing all the 10s in exponential form, which gives us the scientific notation 5 X 107. (Note that 107 is the same as lOx lOx 10x lOx 10 X 10 X 10. Table A. 1 shows the exponential form of some other large and small numbers.) Likewise, the small number 0.0005 is mathematically equal to 5 divided by 10 X 10 x 10 X 10, which is 5/104. Because dividing by a number is exactly equivalent to multiplying by the reciprocal of that number, 5/104 can be written in the form 5 X 10-4, and so in scientific notation 0.0005 becomes 5 X 10-4 (note the negative exponent). 

A2 appendix a scientific notation is used to express large and small numbers... 

The numbers that scientists use range from enormous to extremely tiny. The distances between the stars are literally astronomical—the star nearest to the sun is 23 500 000 000 000 mi from it. As another example, the number of atoms of calcium in 40.0 g of calcium is 602 000 000 000 000 000 000 000, or 602 thousand billion billion. The diameter of one calcium atom is about 0.000 000 02 cm. To report and work with such large and small numbers, scientists use exponential notation. A typical number written in exponential notation looks as follows ... 

In computing the internal solution the starting value of u ik, r) at very small r is arbitrary. The normalisation is given by (4.67). However, in order to avoid computational problems associated with large and small numbers it is convenient to use the first of equns. (4.63) as the starting condition. 

In using such large and small numbers, it is inconvenient to write down all the zeroes. In scientific (exponential) notation, we place one nonzero digit to the left of the decimal. 

Traditionally, for the sake of accuracy, the calculation of the current is carried out from the surface fluxes of the electroactive species such that the product of large and small numbers is avoided and higher-order approximations for the first derivative at the electrode surface can be employed... 

The prefixes in Table 2.4 are represented by the powers of 10 used in scientific, or exponential, notation for writing large and small numbers. For example, 10 = 10 X 10 X 10 = 1000. Appendix B reviews this notation. 

Scientific notation, in which large and small numbers are represented by a number between 1 and multiplied by 10 with an exponent, is reviewed in Appendix B. 

Scientific notation, also known as exponential notation, is a way of representing large and small numbers as the product of two terms. The first term, the coefficient, is a number between 1 and 10. The second term, the exponential term, is 10 raised to a power—the exponent. For example. 

In scientific measurement and calculations, we often encounter very large and very small numbers—for example, 0.00000384 and 602,000,000,000,000,000,000,000. These numbers are troublesome to write and awkward to work with, especially in calculations. A convenient method of expressing these large and small numbers in a simplified form is by means of exponents, or powers, of 10. This method of expressing numbers is known as scientific, or exponential, notation. 

Scientific notation is a simple way to write and keep track of large and small numbers without a lot of zeros. It provides a short cut to recording results and doing calculations. The ease of this method is shown below. 

The prefixes in boldface (heavy) type are the most common ones. The use of exponents to express large and small numbers is discussed in Section 1.7. 

Handling Numbers Scientific notation is used to express large and small numbers, and each number in a measurement must indicate the meaningful digits, called significant figures. 

Scientific Notation Writing Large and Small Numbers 12 2.5 The Basic Units of Measurement 22 2.10 Numerical Problem-Solving... 

Scientific Notation Writing Large and Small Numbers... 

In chemistry, we use numbers that are very large and very small. We might measure something as tiny as the width of a human hair, which is about 0.000 008 m. Or perhaps we want to count the number of hairs on the average human scalp, which is about 100 000 hairs (see Figure 2.5). In this text, we add spaces between sets of three digits when it helps make the places easier to count. However, we will see that it is more convenient to write large and small numbers in scientific notation. 

Q Why are large and small numbers written in scientific notation ... 

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