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**Measurement Scientific Notation Precision**

Rules for addition and subtraction Significant Digits Rules for multiplication and division

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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?

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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

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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

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**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

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Low precision balance

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**High precision balance**

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**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

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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

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**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

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**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

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**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

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