In Physics what does "Significant Digits" mean?

Question

So on the first day of High School, my Adv. Physics teacher immediately gave us some vocabulary to do. The other words are easy to comprehend and understand, but one word keeps on puzzling me. I read the definition over over, and re-read the examples, and yet I still don't understand.

The definition inside the textbook said (I'M TYPING EXACTLY WHAT THE TEXTBOOK SAY)

Significant Digits: The result of any mathematical operation with measurements never can be more precise than the least precise measurement involved in the operation.

Example: Suppose you use a meter stick to measure a pen, and you find that the end of the pen is just past 14.3 cm. This measurement has three valid digits in a measurement are called significant digits. The last digit given for any measurement is the uncertain digit. All nonzero digits in a measurement are significant.

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Are all zero significant? No. For example, in the measurement 0.0860 m, the first two zeros serve only to locate the decimal point and are not significant. The last zero, however, is the estimated digit, and is significant. The measurement 172,000 m could have 3,4,5, or 6 significant digits. The ambiguity is one reason to use scientific notation: it is clear that the measurement 1.7200 x 10^5 m has five significant digits.

Arithmetic with significant digits: When you perform any arithmetic operation, it is important to remember that the result never can be more precise than the least precise measurement.

To add or subtract measurements. first perform the operation, then round off the result to correspond to the least-precise value involved. For example, 3.86 m + 2.4 m = 6.3 because the least precise measure is to one tenth of a meter.

To multiply or divide measurements, perform the calculation and then round to the same number of significant digits as the least precise measurement. For example. 409.2 km/ 11.4 L = 35.9 km/L, because the least-precise measure has three significant digits.

Can someone simplify this into easier terms, and relate it to real life?

THANK YOU.

Answer 1

the significant digits represent the valid digits of a number.

-nonzero digits are always significant.

-all final zeros after the decimal points are significant.

-zeros between two other significant digits are always significant.

-zeros used solely for spacing the decimal point are not significant.



in addition and subtraction, round up your answer to the least precise measurement.



24.686 + 2.343 + 3.21 = 30.239 = 30.24



because 3.21 is the least precise measurement.



in multiplication and division, round it up to the least number of significant digits.



3.22 * 2.1 = 6.762 = 6.8



because 2.1 contains 2 significant digits.



in a problem with the mixture of addition, subtraction, multiplication or division, round up your answer at the end, not in the middle of your calculation.



3.6 * 0.3 + 2.1 = 1.08 + 2.1 = 3.18 = 3.2.





:)

Answer 2

Definition Of Significant Digits

Answer 3

Significant Digits Definition

Answer 4

Significant figures are referring to the accuracy of the result.

If you have 12.6 cm, this means that there is 12.6 cm +/_ .01 cm.



You also have to take into account the uncertainty of a measurement.

So if you have 12.6 cm, you have measured to the nearest millimeter. So if you put 12.60, your answer will be wrong because it is more precise than you are certain of.