Sig Fig

Started by Aditi, April 25, 2024, 10:46:34 PM

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Aditi

Hi, I was wondering how to solve this problem; what are sig figs again? And how would you solve this? I solved all the expressions, which were equivalent to the answer in the problem, which said, "which is not correctly represented by the right number of significant numbers." So I was just confused how to solve this. I submitted the quiz and it said, a. How?

uma

Sig - Fig tells the accuracy of measurement.
If sig - fig are more - more accuracy in the measurement.
Rules for Significant figure:
1.    Any digit that is not zero is significant
1.234 kg - 4 significant figures.
2.    Zeros between non-zero digits are significant
              606 m      -  3 significant figures
3.    Leading zeroes are never counted as sig - fig 
or Zeros to the left of the first nonzero digit are not significant
            0.08 L    --    1 significant figure
4.    Trailing zeroes are counted as sig - fig if there is a decimal or all zeros to the right of the decimal point are significant.
  2.0 mg    --    2 significant figures
5.    Trailing zeroes are not counted as sig -fig if there is no decimal in the number.
100 g      --      1 sig-fig (without decimal)
100. g      --    3 Sig-fig (with decimal)
6.    Exact Numbers or counted numbers are always considered numbers without error and hence have infinite Sig-fig.
In exact number, there is no uncertain digits as these numbers are not measured using a measuring scale.
Examples of exact numbers.
All metric conversions are exact numbers - There are 100 cm in 1 m, A kilogram is 1000 g.
All counted numbers are exact numbers. 12 pencils – infinite sig -fig

Practice: How many significant figures are in each of the following measurements?
Measurements:                          Number of sig-fig
24 mL                                      2 significant figures (all non-zeroes are counted)
50 books                                  Infinite significant figures (exact number has infinite sig -fig)
3001 g                                      4 significant figures (in between zeroes are counted)
0.0320 m3                                3 significant figures (leading zeroes not counted)
6.4 x 104 molecules                2 significant figures
560 kg                                      2 significant figures (trailing zero with no decimal counted)
20 pens                                    Infinite significant figures (exact number has infinite sig -fig)

Multiplication and Division of significant Figures
The number of significant figures in the result is the same as the number in the least precise measurement used in the calculation.
4.51 x 3.6666 = 16.536366= 16.5 (3 sig figs) 6.8 ÷ 112.04 = 0.0606926 =  0.061  2 sig figs 
Rules for addition or Subtraction:
The answer cannot have more digits to the right of the decimal point than any of the original numbers.
21 - 13.8 =7
The result is 7 with no decimal point because the number with the least number of decimal places (21) has none.

A ((2.70/3.00)-2.0) X (1.20)
Apply sig - fig rule step by step --- (0.900-2.0)X (1.20) (put after subtraction only one decimal place)
= -1.1 X (1.20) (after multiplication only two sig -fig)
= -1.3 ( answer must have only two sig- fig)
It means A is not correct.



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