Scientific notation significant digits

Rule 6 When a number is expressed in scientific notation, all digits in the coefficient are taken to be significant ... 

Suppose you must do a calculation using the measurement 200 L. You cannot be certain which zero was estimated. To indicate the significance of digits, especially zeros, write measurements in scientific notation. In scientific notation, all digits in the decimal portion are significant. Which of the following measurements is most precise ... 

In scientific notation the digit term indicates the number of significant figures in the... 

In scientific notation the digit term indicates the number of significant figures in the number. The exponential term merely locates the decimal point and does not represent 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. 

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

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. 

For numbers that are written in scientific notation, only the root portion of the number is considered. (Example 1.605 X 107 would have 4 significant digits.)... 

The Great Lakes contain 22 700 km3 of water. Is there exactly that amount of water in the Great Lakes No, 22 700 km3 is an approximate value. The actual volume could be anywhere from 22 651 km3 to 22 749 km3. You can use scientific notation to rewrite 22 700 km3 as 2.27 x 104 km. This shows that only three digits are significant. (See Appendix E at the back of the book, if you would like to review scientific notation.)... 

What if you were able to measure the volume of water in the Great Lakes You could verify the value of 22 700 km3. Then all five digits (including the zeros) would be significant. Here again, scientific notation lets you show clearly the five significant digits 2.2700 x 104 km3. 

The value 11 cm has the smallest number of significant digits two. Thus, your answer can have only two significant digits. In order to have only two significant digits, you need to put your answer into scientific notation. 

Round to three significant digits and express in scientific notation 1.80 x 101 g/mol... 

Another advantage to scientific notation is that all digits of the coefficient of a number in scientific notation are significant. The exponent determines the magnitude of the number, so any zeros present in the coefficient must be significant. 

One way to resolve this problem is to report the values in scientific notation, where all digits of the coefficient are significant (a) 3.5 x 10 mm,... 

All digits in the coefficient of a properly reported number in scientific notation are significant ... 

The significant figures in a number can be formally established by using scientific notation that is, the rule that the first digit of all numbers is followed by a... 

C. [10 ]—(3.45 x 2.9 = 10.005) We want our answer to show two significant digits, so I put a line over the zero to make it significant. I could have used scientific notation instead, and written 1.0 x 101. 

Let s begin by listing the information that we know and the original formula. Please don t be confused by the use of scientific notation in the problem. It is simply used to indicate a certain number of significant digits. 

Solve the following problems and express the answers in scientific notation with the proper munber of significant digits. 

Solve the following problems and express the answers in scientific notation with the proper number of significant digits, a) (2.00 X 10 cm)(2.05 X 10 cm)... 

If it is not obvious then the number of significant figures is best determined by writing the result in scientific notation (i.e., x.xxx x 10y) and counting the digits. 

Expressing the concentration of copper in scientific notation, 0.00000572 becomes 5.72 x 10 6 M. Hence there are three significant figures, the digit before the decimal point and the two digits after the decimal point. 

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