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1.5 Energy: A Fundamental Part of Physical and -- Part 3

- Thanks to the Clean Air Act and its amendments, cleaner air has been created in all major U.S. cities over the last 30 years.
- The number of digits to which the measurement is reported is the second thing you might notice.
- The number of digits indicates the certainty of the measurement.

- The first set of data is reported to the nearest 0.1 parts per million, while the second set is reported to the nearest 1 parts per million.
- Scientists report measured quantities in a standard way.
- More digits, more certainty, fewer digits, less certainty are reflected in the number of reported digits.
- The numbers are written so that the uncertainty is in the last reported digit.

- The scientists reported the 2010 carbon monoxide concentration as 1.9 parts per million.
- The carbon monoxide con centration can be between 2.0 and 3.0 parts per million.
- If the reported value was between 1 and 3 parts per million, this would mean 21 parts per million.

- Every digit is certain except the last, which is estimated.

- The first three digits are certain.

- The number of digits reported depends on the measuring device.

- Consider weighing a nut on two different balances.

- For the balance on the top, we divide the space between the 1- and 2-g marks into ten equal spaces and estimate the pointer at about 1.2 g. The point is between the 1.2-g mark and the 1.3-g mark.

- The reading is 1.27 g.

- We divide the space between the two marks into ten equal spaces and estimate the third digit.
- The figure shown is 1.27 g.

- There are markings every 0.1 mL on the graduated cylinder shown in the right margin.

- The volume should be reported to the correct number of digits.

- If you divide the space between the markings into ten equal spaces, you can estimate the next digit.
- You should report the result as 4.57 liters.

- A one-unit difference in the last digit is acceptable if the last digit is estimated and different people estimate it differently.
- You would have mis reported the measurement if you wrote 4.63 mL.

- The temperature should be shown in the right margin and the number of digits should be shown in the left margin.

- The precision of a measurement depends on the instrument used to make the measurement and must be preserved, not only when recording the measurement, but also when performing calculations that use the measurement.
- The number 23.56 has four significant figures while the number 23.5 has three.
- To determine the number of significant figures in a number containing zeroes, we distinguish between zeroes that are significant and those that simply mark the decimal place.

- The nonzero digits are significant.

- The zeroes between two nonzero digits are significant.

- The leading zeroes are not significant.

- They only serve to find the point.

- Trailing zeroes after a decimal point are always significant.

- If the 1200, some textbooks put a decimal point after one or more trailing zeroes.

- There are 4 significant figures zeroes.
- It's common in some books, but we don't do it in this one.

- An exact number has an unlimited number of significant figures.
- The numbers come from three sources.
- 3 atoms means 3.00000.

- The number of centimeters in 1 m is defined as 100.0000.

- Rule 1 states that the two 4s and the 5 are significant.
- Rule 4 states that the trailing zero is significant.
- The leading zeroes are not significant because they only mark the decimal place.

- The five and three are significant, as are the three interior zeroes.

- There is an unlimited number of significant figures.

- Rule 1 says that the 1 is significant.
- Rule 4 states that the trailing zeroes are significant.

- Rule 1 states that the 2 is significant.
- The leading zeroes are not significant because they only mark the decimal place.

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