HINTS ON SIGNIFICANT FIGURES
DR. SUSAN PETRO
Hint #1 - Moving the decimal point doesn't change significant figures
Example #1 - 723.2 g written as 0.7232kg - both have four significant figures
When are zeros significant?
Hint #2 - Zeros sandwiched between two significant digits are always significant
Example # 1 - 3.0002 - 5 significant figures
Example #2 - 8903 - 4 significant figures
Example #3 - 650.007 - 6 significant figures
Hint #3 - Trailing zeros to the right of the decimal point are always significant
Example #1 - 3.0 - 2 significant figures
Example #2 - 12.000 - 5 significant figures
Example #3 - 2000.0 - 5 significant figures (Hints #2 and #3 - since the zero to the
right of the decimal point is significant, the three zeros to the right
of the 2 are sandwiched between two significant figures and are
therefore significant)
Hint #4 - Leading zeros are never significant.
Example #1 - 0.0005 - one significant figure
Example #2 - 0.89 - two significant figures
Example #3 - 0.0060600 - five significant figures (Hints #2 and #3 - zero between
the two sixes is significant and two trailing zeros to the right of the
decimal point are significant.
Hint #5 - Trailing zeros that appear to the left of the decimal point can't be assumed
to be significant
Example #1 - 2000 - At least 1 significant figure
Example #2 - 1230 - At least 3 significant figures
Example #3 - 92,900,000 - At least 3 significant figures
Hint #6 - Any zeros that vanish when you convert a measurement to scientific
notation are not significant figures.
Example #1 - 1000 converted to scientific notation - 1 x 103 - At least 1
significant figure
Example #2 - 0.00053 converted to scientific notation - 5.3 x 10-4 - 2 significant
figures
Example #3 - 130.00200 converted to scientific notation - 1.3000200 x 102 - 8
significant figures
Example #4 - 0.007010 converted to scientific notation - 7.010 x 10-3 - 4
significant figures
Hint # 7 – When performing additions or subtractions, the answer should contain
no more decimal places than the number with the least number of digits
following the decimal place.
Example #1 – 7.2°C subtracted from 7.663°C yields a correct answer of 0.5°C
not 0.463°C nor 0.46°C. The least precise measurement of the two
original temperatures we were measuring is 7.2°C which is to the
tenths position so that is how precise our answer can be. Our
answer in this case had only one significant figure
Example #2 – 8.2mm + 10.33mm + 23.539mm yields a correct answer of 42.1mm
not 42.069mm nor 42mm. Note there are 3 significant figures in
the answer, because our least precise original measurement, 8.2mm
only went to the tenths position so we can only go to the tenths
position in the answer.
Example #3 - 150.0 g + 0.507 g = 150.5 g not 150.507g. The least precise
measurement of the original two was 150.0g which went out to the
tenths position so our answer goes out to the tenths position.
Example #4 – 1.26ml + 102.3ml = 103.6ml Note there are 4 significant figures in
the answer not 3 significant figures. Our answer goes to the tenths
position because the least precise of our original two volumes went
out to the tenths position.
Hint #8 – When performing multiplication or division with numbers having
different levels of significant figures, express the answer using the number
of significant figures associated with the least precise value.
Example #1 – 102.35 ÷ 15.72 = 6.511 The least precise value had 4 significant
figures so the answer has four significant figures.
Example #2 – 3.69 X 2.3059 = 8.51 the least precise value had three significant
figures so the answer has three significant figures.
Hint #9 - When multiplying or dividing a measurement with an exact number, the
result should be rounded to the same number of sig figs as the
measurement.
Example #1 – If you put six mice on a balance and found the combined weight to
be 32.51 grams what would be the average weight of one mouse?
Six is an exact number, that’s how many mice there are, so the fact
that 6 has 1 significant figure would not be taken into account. The
answer would be 5.418g, which has the same number of significant
figures, four, as the combined weight of the mice. The answer
would not be 5g.
Hint #10 – When the value you intend to round off is a five, you MUST also look at
the value to the left of the five. If it is even, you round down. If it is odd,
you round up. Zero is considered even.
Example #1 - Round 37.6514 to three significant figures. Look at the fourth digit. It is a
5, so now you must also look at the third digit. It is 6, an even number, so
you simply drop the 5 and the figures that follow it. The original number
becomes 37.6
Example #2 - Round 524.435 to five significant figures. To do this, you must look at the
sixth digit. It is a 5, so now you must look at the fifth digit also. That is a 3,
which is an odd number, so you round the original number up to 524.44.