Notation decimal

Abbreviation Name Scientific Notation Decimal Notation... 

In science, we often encounter very large and very small numbers. Written in standard decimal notation, these numbers can be cumbersome. There are, for example, about 33,460,000,000,000,000,000,000 water molecules in a thimbleful of water, each having a mass of about 0.00000000000000000000002991 gram. To represent such numbers, scientists often use a mathematical shorthand called scientific notation. Written in this notation, the number of molecules in a thimbleful of water is 3.346 X 1022, and the mass of a single molecule is 2.991 X 10 23 gram. 

One common representation of numbers is decimal notation. Typical examples are such large numbers as 807,267,434.51 and 3,500,000, and such small numbers as 0.00055 and 0.0000000000000000248. Decimal notation is often awkward to use, and it is embarrassingly easy to make foolish mistakes when carrying out arithmetical operations in this form. Most hand calculators will not accept extremely large or extremely small numbers through the keyboard in decimal notation. 

Some calculators make it possible for you to choose in advance that all results be displayed in scientific notation (or decimal notation), regardless of which notation you use for entering numbers You can also choose how many decimal places (usually up to a maximum of 8) will be displayed in decimal notation, or in the lefthand factor of scientific notation If your calculator has... 

Let us divide by 10 again. We now know that every time we divide by 10, the power of 10 goes down by 1. Thus 10 1 divided by 10= 10-2 10 2 written in decimal notation as 0.01 . 

Convert each of the following values to ordinary (decimal) notation ... 

Some calculators display answers in decimal notation unless they are programmed to display them in scientific notation. If a number is too large or too small to fit on the display in decimal format, the calculator will use scientific notation automatically. To get a display in scientific notation for a reasonably sized decimal number, see the owner s manual. If an easy conversion is not available, multiply the decimal value by 1 X 10 ° (if the number is greater than 1) or 1 X 10 ° (if the number is less than 1), and mentally subtract or add 10 to the resulting exponent. 

The factor 6 is a pure integer. Estimate the value of R without using a calculator, following the procedure outlined in Section 2.5b. Then calculate R, expressing your answer in both scientific and decimal notation and making sure it has the correct number of significant figures. 

Although this system seems cumbersome to people who are used to the decimal notation system, it is perfectly suited for the ways that computers manipulate electric currents to process large quantities of data at very fast rates. 

This expression tells us that the gamma-ray intensity reduces in accordance with the decimal notation. For example, at twice and three times as large a shield thickness as TVT, the gamma-ray intensity reduces to 1/100 and 1/1000 of the incident intensity, respectively. 

Decimal notation for both integers and fractions is an everyday familiarity. It is, however a specific case of a more general notation in which digits are used in a way where their positions carry information as well as their typography. 

Scientists and engineers are frequently called upon to use very large or very small numbers for which ordinary decimal notation is either awkward or impossible. For example, to express Avogadro s number in decimal notation would require 21 zeros following the number 602. In scientific notation the number is written as a multiple of two numbers, the one number in decimal notation and the other expressed as a power of 10. Thus, Avogadro s number is written as 6.02 X 1Other examples are... 

The number in the exponent is equal to the number of places the decimal must be shifted to convert a number from scientific to purely decimal notation. The shift is... 

The last two examples demonstrate that the logarithm of a number is the sum of two parts, a characteristic located to the left of the decimal point and a mantissa that lies to the right. The characteristic is the logarithm of 10 raised to a power and serves to indicate the location of the decimal point in the original number when that number is expressed in decimal notation. The mantissa is the logarithm of a number in the range between 0.00 and 9.99... Note that the mantissa is always positive. As a consequence, the characteristic in the last example is —6 and the mantissa is +0.30. 

What is the advantage of using scientific notation over decimal notation ... 

Half-life in decimal notation, ps = microseconds ms = milliseconds s = seconds m = minutes h = hours d = days and y = years. For quasi-stable nuclides, the measured width at half maximum of the energy resonance is given... 

Half-life in decimal notation, ps = microsecond ms = millisecond s = second m = minute h = hour d = day y = year. 

When the number 4.512 x 10 is written in ordinary decimal notation, it is expressed as... 

You are accustomed to writing numbers in decimal notation, for example 123 677.54 and 0-001678. in working with large numbers and small numbers, you will fmd it convenient to write them in a (Afferent way, known as scientific notation oc stanJerd form. This means writing a number as a product of two factors. In the first factor, the Mimai point comes after the first digit. The second factor is a multiple of ten. For example, 2123 = 2.123 X 10 and 0.000167 = 1.67 X 10. lO means lOX lOX 10, and 10 means 1/(10 X 10 X 10 X 10). The number 3 or —4 is cdled the exponent, and the number 10 is the base. KH is referred ro as 10 to the power or 10 CO the third power . You will have noticed that, if the exponent it increased by 1, the decimal point must be moved one place to the left. 

Solution Writing both numbers in decimal notation, we have... 

Real Numbers When a fraction is expressed as a decimal, it either terminates or repeats. For example, the fraction 0.75 terminates and the fraction = 0.727272... repeats (denoted 0.72). Many numbers in the number line do not repeat and do not terminate y/2 — 1.4142135..., /24 = 4.8989794..., and 7T = 3.1415926... are some examples. Numbers whose decimal notation does not terminate and does not repeat are called irrational numbers. Real numbers are the set of all rational numbers combined with the set of all irrational numbers. 

In order to make them easier to manage, IP addresses are usually described by the four bytes they contain, aU specified in decimal notation, and separated by single dots. Examples of IP addresses are ... 

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