Scientific notation expressing number

Scientific notation expresses numbers as a multiple of two factors a number between 1 and 10 and ten raised to a power, or exponent. The exponent tells you how many times the first factor must be multiplied by ten. The mass of a proton is 1.627 62 X 10 kg in scientific notation. The mass of an electron is 9.109 39 X 10 kg. When numbers larger than 1 are expressed in scientific notation, the power of ten is positive. When numbers smaller than 1 are expressed in scientific notation, the power of ten is negative. 

In the addition or subtraction of numbers expressed in scientific notation, all numbers should first be expressed with the same exponent ... 

When adding or subtracting numbers in scientific notation, the numbers must be converted to the same power of 10 as the measurement with the greatest power of 10. Once the numbers are all expressed to the same power of 10, the power of 10 is neither added nor subtracted in the calculation. 

A When adding and subtracting numbers in scientific notation, express the numbers to the same power of 10. For example,... 

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... 

In scientific notation, a number is expressed as e. product ofitwo numbers. By convention, the first number, called the digit term, is between 1 and 10. The second number, called the exponential term, is an integer power of 10. Some examples follow. 

It is likely that you have already seen numbers expressed in scientific notation on your calculator. With only 8 or 9 spaces to display numbers, calculators must resort to scientific notation to show very small or very large numbers. In scientific notation a number is expressed in this form... 

Scientific notation expresses a number as a product of a number between 1 and 10 and the appropriate power of 10. 

Scientific notation expresses a number in the form N X 10 a convenient method for representing a very large or very small number and for easily indicating the number of significant figures. 

When a large or small number is written in standard scientific notation, the number is expressed as the product of a numher between 1 and 10, multiplied by the appropriate power of 10. For each of the following numbers, indicate what number between 1 and 10 would be appropriate when expressing the numbers in standard scientific notation. 

Multiplication and division in scientific notation when numbers expressed in scientific notation are being multipUed, the following general rule is very useful ... 

Numbers such as these are very awkward to work with. For example, neither of the numbers just written could be entered directly on a calculator. Operations involving very large or very small numbers can be simplified by using exponential (scientific) notation. To express a number in exponential notation, write it in the form... 

Scientific notation uses exponents to express numbers. The number 1,000, for instance, is equal to 10 x 10 x 10, or 10. The number of zeros following the 1 in 1,000 is 3, the same as the exponent in scientific notation. Similarly, 10,000, with 4 zeros, would be 10 , and so on. The same rules apply to numbers that are not even multiples of 10. For example, the number 1,360 is 1.36 x 10. And the number of atoms in a spoonful of water becomes an easy-to-write 5 X 10. ... 

Most people find that writing 300000000 ms-1 is a bit long winded. Some people do not like writing simple factors such as G for giga, and prefer so-called scientific notation. In this style, we write a number followed by a factor expressed as ten raised to an appropriate power. The number above would be 3.0 x 108 ms-1. 

Round the following numbers to the number of significant figures indicated and express in scientific notation. 

Another way to determine the number of significant figures in a number is to express it in scientific (exponential) notation. The number of digits shown is the number of significant figures. For example, 2.305 X 10 5 would contain four significant figures. 

Any zero to the right of nonzero digits and to the left of a decimal point and not covered by rule 2 may or may not be significant, depending on whether the zero is a placeholder or actually part of the measurement Such a number should be expressed in scientific notation to avoid any confusion. 

For example, to express 6,403,500,000 in scientific notation, first change the number to a decimal between 1 and 10, that is 6.4035. Now, multiply this decimal by a power of 10, determined by the number of placeholders the decimal was moved. This is a large number, so the power of 10 will be positive. 

Since the decimal point was moved nine places to the left, the power of 10 is nine, and the number written in scientific notation is 6.4035 x 109. Note that even though 64.035 x 108 is another form of the same number, this is NOT scientific notation, since the decimal number is not between one and ten. As an example of a very small number, consider changing 0.000006007 to a number expressed in scientific notation. Write the num-... 

Scientific notation is a shorthand way to express very large or very small numbers. The notation expresses a number as a decimal (between one and ten), multiplied by an appropriate power of ten. 

Add, subtract, multiply, or divide. Round off your answer, and express it in scientific notation to the correct number of significant digits. 

Addition or subtraction gets easier when you express your numbers as coefficients of identical powers of 10. To wrestle your numbers into this form, you may need to use coefficients less than 1 or greater than 10. So scientific notation is a bit too strict for addition and subtraction, but exponential notation still serves you well. 

When you know how to express your numbers in scientific notation and how to distinguish between precision and accuracy (we cover both topics earlier in this chapter), you can bask in the glory of a new skill using scientific notation to express precision. The beauty of this system is that simply by looking at a measurement, you know just how precise that measurement is. 

X10" First, convert each number to scientific notation 8.09x 10 and 2.03X10. Then divide the coefficients 8.09/2.03 = 3.99. Next, subtract the exponent on the denominator from the exponent of the numerator to get the new power of 10 10 = 10" Join the new coefficient with the new power 3.99x10 . Finally, express gratitude that the answer is already conveniently expressed in scientific notation. 

Scientific notation was developed to allow scientists, mathematicians, and people like you and me to write really, really large numbers or teeny, tiny small numbers without using up a full page to express the numbers for the reader. 

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

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

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