Significant figures scientific notation

Scientific Notation Significant Figures in Calculation of Results Rounding Off Numbers... 

Scientific Notation Significant Figures Accuracy and Precision... 

In general, any ambiguity concerning the number of significant figures in a measurement can be resolved by using exponential notation (often referred to as scientific notation ), discussed in Appendix 3. 

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. 

Crunching numbers in scientific and exponential notation Telling the difference between accuracy and precision Doing math with significant figures... 

If a number is already written in scientific notation, then all the digits in the coefficient are significant. So the number 3.5200X 10" has five significant figures due to the five digits in the coefficient. 

The raw calculation yields 4,147.2 inches, which rounds properly to four significant figures as 4,147 inches, or 4.147x10 inches in scientific notation. 

One further point about significant figures Certain numbers, such as those obtained when counting objects, are exact and have an effectively infinite number of significant figures. For example, a week has exactly 7 days, not 6.9 or 7.0 or 7.1, and a foot has exactly 12 in., not 11.9 or 12.0 or 12.1. In addition, the power of 10 used in scientific notation is an exact number. That is, the number 103 is exact, but the number 1 X 103 has one significant figure. 

The diameter of the earth at the equator is 7926.381 mi. Round off this quantity to four significant figures to two significant figures. Express the answers in scientific notation. 

We often use scientific notation to express very large or very small numbers, indicating the number of significant figures by the number multiplied by 10X. Thus, for example,... 

One operational way to identify significant zeros is to convert the number into scientific notation. If the decimal point does not cross a zero when converting a number into scientific notation, the zero is always significant. Some additional examples are given below (significant figures are in bold). 

A couple of comments are in order here. First, did you notice the value of the pH is the same as the absolute value of the exponent This will always be true when the first part of the scientific notation is exactly 1. The second comment relates to significant figures. There are two significant figures in the molarity measurement of 1.0 x 10 3 M. There are also two significant figures in the pH value of 3.00. Finally, pH values have no intrinsic units. Logarithms represent pure numbers, and as such, have no units. 

In this unit you will find explanations, examples, and practice dealing with the calculations encountered in the chemistry discussed in this book. The types of calculations included here involve conversion factors, metric use, algebraic manipulations, scientific notation, and significant figures. This unit can be used by itself or be incorporated for assistance with individual units. Unless otherwise noted, all answers are rounded to the hundredth place. The calculator used here is a Casio FX-260. Any calculator that has a log (logarithm) key and an exp (exponent) key is sufficient for these chemical calculations. 

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