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 When we count we use exact numbers  If we count people we have exactly 4 people  There is no uncertainty about this number of people.  Measurements using an interval scale (like a ruler) has some uncertainty  Is it 29.68cm or is it 29.67cm?  This involves some estimation on the last digit

 Invented in order to compare quantities  The metre was once defined as the distance between two scratches on a bar of platinum- iridium alloy at 0 o C  All other measurements of distance are estimated  Not all measurements, however, are known to the same accuracy  Accuracy is how close the measurement is to the real value. (Sometimes the real value is not known)  A micrometer, for example, will yield a more accurate measurement of a hair's diameter than will a metre stick

 Significant digits tell us something about how the measurement was made  A better instrument allows us to make better measurements and we record a greater number of significant digits in reporting this value  A metre stick would only allow us to record the thickness of a hair as 0.1mm  A micrometer allows us to record the thickness as 0.137 mm  This measurement is closer to the true value and is a more accurate measurement

 Is it possible to be too accurate?  When is it not suitable to use a more precise measuring tool?  For each measurement would you use a micrometer or a metre stick?  Length of table  Width of fruit fly  Thickness of a penny  Width of hand  Distance to the sun  Having the length of a table recorded at 1.2345678909876m is not needed for most cases  A recording of 1.23m is sufficient most of the time

2m 20cm406080 3m  Suppose the length of a table is measured with a ruler calibrated to 10 centimetres  The table is definitely less than 2.8 metres but greater than 2.7 metres

 Is the extra length 0.04 or is it 0.05?  We make the best possible estimate  A proper measurement would be recorded as 2.74 metres. This has 3 Sig-Figs  Where did the 0.04 come from? I thought the ruler could only do 10 centimeters at a time?  This indicates the table has a length of 2 metres plus 70 centimetres plus a little bit more  A measurement of the same table with a ruler calibrated to centimetres could yield 2.742 metres. This has 4 Sig-Figs 2m 20cm406080 3m

1. All non-zero digits are significant a. Eg.374 (3 sig-figs) b. 8.1 (2 sig-figs) c. 8.365 X 10 4 (4 sig-figs) 2. All zeroes between non-zero digits are significant (Captured Zeros) a. Eg.50407 (5) b. 8.001 (4) c. 9.05 X 10 4 (3)

3. Leading zeroes in a decimal are not significant a. Eg.0.54 (2) b. 0.0098 (2) c. 0.05 X 10 -7 (1) ( Not proper Scientific notation) 4. Trailing zeroes are significant only if they are to the right of a decimal point a. Eg.2370 (3) b. 16000 (2) c. 16.000 (5) 5. In numbers greater than 1, trailing zeroes are not significant unless stated so a. Eg. 37000 (2)

 The last three zeroes may or may not be part of the measurement.  To show that they are, we use scientific notation. All the zeroes written in the number in scientific notation are significant.  37000 with 3 sig. digits would be 3.70 x 10 4  37000 with 4 sig. digits would be 3.700 x 10 4  37000 with 5 sig. digits would be 3.7000 x 10 4  37000.0 has 6 sig. digits  Exact Numbers do not affect Sig-Figs  If I count 4 people, I have exactly 4, not 4.01 or 3.99  If I take the average of 7 tests, that 7 is an exact number, will not affect sig-figs in any way.

 Round each value to 3 sig figs  1.234 1.23  9.865 9.87  0.07888 0.0789  0.5399 0.540  12990 1.30 x 10 4

 General Rules:  Add or subtract as normal.  Count the number of digits to the right of the decimal.  The answer must be rounded to contain the same number of decimal places as the value with the LEAST number of decimal places

 Example  12.0 + 131.59 + 0.2798 = ?  Add as normal: 12.0 + 131.59 + 0.2798 = 143.8698  The least number of decimal places is 12.0, with one decimal place  Round to the least number of decimal places  Final Answer = 143.9  0.0998 – 1.0  = -0.9002  = -0.9  5.4 x 10 2 + 2.8 x 10 1  = 568  = 570

 General Rules:  Multiply or divide as normal.  Count the number of significant figures in each number.  The answer must be rounded to contain the same number of significant figures as the number with the LEAST number of significant figures

 Example  51.3 × 13.75 = ?  Multiply as normal: 51.3 × 13.75 = 705.375  The least number of significant figures is 3 in 51.3  Round to the least number of significant figures  Final Answer= 705

 Example  2.00 x 7.00  = 14  = 14.0  (3.0×10 12 ) / (6.02×10 23 )= ?  Put the numbers into your calculator as usual: 3.0×10 12 ÷ 6.02×10 23 = 4.98338×10 −12  The least number of significant figures belongs to 3.0×10 12 with 2 sig figs  Final Answer = 5.0×10 −12  250 x 4.0  = 1000  = 1.0 x 10 3

 Using proper sig-figs, find how many seconds are in 1 year (365.25 days)  = 31557600  = 31558000

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