Standard scientific notation

Each entry contains the title of the article, the author(s) and the bibliographic source which is given in abbreviated form according to standard scientific notation. The present chapter does not use the reference conventions that have been adopted elsewhere throughout this treatise as this chapter is essentially its own bibliography. 

Write the number 0 00055 in standard scientific notation SOLUTION ... 

Write the number in standard scientific notation Standard notation isn t required, but it is a good habit to acquire... 

To multiply two numbers, put them both in standard scientific notation. Then multiply the two lefthand factors by ordinary multiplication, and multiply the two righthand factors (powers of 10) by the multiplication law for exponents — that is, by adding their exponents. 

Write each number in standard scientific notation. This gives... 

To divide one number by another, put them both in standard scientific notation. Divide the first lefthand factor by the second, according to the rules of ordinary division. Divide the first righthand factor by the second, according to the division law for exponents—that is, by subtracting the exponent of the divisor from the exponent of the dividend to obtain the exponent of the quotient. 

First, rewrite all numbers in standard scientific notation ... 

Note that the characteristic is determined by the power to which 10 is raised (when the number is in standard scientific notation), and the mantissa is determined by the log of the lefthand factor (when the number is in scientific notation). It is these properties that make it so easy to find the logarithm of a number using a log table. Here is how you can do it. 

A. Express each of the following in standard scientific notation, and also give the answer in that notation. 

The exponent of 10 is the number of places the decimal point must be shifted to give the number in long form. A positive exponent indicates that the decimal point is shifited right that number of places. A negative exponent indicates that the decimal point is shifited left. When numbers are written in standard scientific notation, there is one nonzero digit to the left of the decimal point. 

For each of the following numbers, if the number is rewritten in standard scientific notation, what will be the value of the exponent (for the power of 10) ... 

Round off each of the following numbers to the indicated number of significant digits, and write the answer in standard scientific notation. 

For each of the following numbers, by how many places must the decimal point be moved to express the number in standard scientific notation In each case, will the exponent be positive, negative, or zero ... 

Write each of the following numbers in standard scientific notation. See the Appendix if you need help multiplying or dividing numbers with exponents. 

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