1. Measurement Scientific Notation Precision
Rules for addition and subtraction
Significant Digits
Rules for multiplication and division

2. Scientific Notation
Measurements in chemistry generate values that range from incredibly large to incredibly small values
For example:
1 gram of iron contains about atoms and
1 atom of iron weighs about grams
Rather than write all those zeros, scientists write these values in scientific notation
The general form for scientific notation is _._ _ x 10?

3. For numbers greater than one: move the decimal to the left until there is 1 digit in front of it. The number of places the decimal moves becomes the exponent on the 10.
= 1.5 x 1022 Try entering into your calculator and then ask it to put it into scientific notation Try: = 5.6 x x 105 = 7.43 x x 1010 = 5.6 x =5 x 108

4. For numbers less than one: move the decimal to the right until there is 1 digit in front of it. The number of places the decimal moves becomes the exponent on the 10, except that now the exponent is negative.
= 1.5 x Try: = 4.5 x x = 3.60 x x 10-6 = 5.45 x = 5 x 10-7

5. Precision Depends on the graduations of the measuring device
Is the place value of the last measurable digit
For example, cm is more precise than cm

6. Low precision balance

7. High precision balance

8. Adding or subtracting measurements of different precision:
The answer is rounded to the same precision of the least precise measurement
For example:
11.7cm cm cm. Your calculator will give the answer cm BUT the correct answer is
15.5cm
Try: g g
= 31.4g

9. Significant Digits
The more digits that are in a measurement, the more certain you are about the measurement.
For example, if the banana on the low precision balance were to be placed on the high precision balance, its mass may register g rather than 186 g
The certainty of the measurement is communicated by the number of significant digits recorded.
There is more certainty in the second measurement because 5 significant digits (185.89) have been recorded rather than 3 (186).
When zeros have been recorded in a measurement, they present a problem as to whether they are considered as significant digits

10. Rule to determine whether a digit is significant
All non-zero digits are significant
186 has 3 significant digits; has 5 significant digits
Zeros between non-zero digits are significant
1806 has 4 significant digits; has 6 significant digits
Any zero after a decimal point that also has significant digits before the decimal point is significant
623.0 has 4 significant digits; has 6 significant digits
Any zero before a decimal point and before other significant digits is not significant
0.632 has 3 significant digits; has 3 significant digits; has 5 significant digits

11. Writing the value in scientific notation makes it clearer:
Measurements with no decimal and ending in zeros make it difficult to determine the precision of the measuring device.
For example, 1860 could be considered to have 3 or 4 significant digits depending on the precision of the measuring device
Writing the value in scientific notation makes it clearer:
1.860 x 103 or 1.86 x 103
If the above example is not written in scientific notation, it will be assumed that the zero is significant

12. Multiplying or dividing measurements of different degrees of certainty:
The final answer has the same number of significant digits as the least number in the question
For example:
2/6 = …..
would be written 0.3
2.1/6.3
= 0.33
2.00/6.0
52 x 16 = 832
would be written 8.3 x 102 or 830