1.3: significant figures in measurements
significant figures
significant figures: the digits in a measurement that were actually measured
all known numbers + one estimated number
communicate the uncertainty of a measurement
reflect the precision of the instrument with which a measurement is made
determining which digits are significant
all non-zero digits
eg. 1245 (4 significant figures)
2.3 (2 significant figures)
all captive zeros (zeros between non-zero digits)
2021 (4 significant figures)
5000.1 (5 significant figures)
leading zeros are never significant
0.0012 (2 significant figures) → placeholders
zeros at the end of a number (trailing zeros) are
not significant if there is no decimal point in the number:
230 (2 significant figures)
7000 (1 significant figure)
significant if there is a decimal point in the number
3.230 (4 significant figures)
7.0 (2 significant figures)
scientific notation
used to describe very large or very small numbers because
it’s time-consuming to read/write
easy to lose track of zeros and mess up
numbers are expressed with
one digit to the left of the decimal, multiplied by a power of ten
eg. 4.59x10^5
4.59 is the significand, 10 is the base, and 5 is the exponent.
if x > 1, the exponent is positive, and if x < 1, the exponent is negative
scientific notation and significant figures
significand determines number of significant figures
eg. 4.590 x 10^5 => 5 sigfigs (4.590)
significant figures in calculations
addition/subtraction—answer is rounded to the smallest significant decimal place
multiplication/division—answer is rounded to the number of digits that corresponds with the least number of significant figures in any of the numbers used in the calculation
dimensional analysis
used to convert a measurement from one unit to another using conversion factors
conversion factor: a ratio of equivalent measures (numerator = denominator)
when a measurement is multiplied by a conversion factor, the expression of measurement changes (because the units change) but the actual quantity measured remains the same
1.3: significant figures in measurements
significant figures
significant figures: the digits in a measurement that were actually measured
all known numbers + one estimated number
communicate the uncertainty of a measurement
reflect the precision of the instrument with which a measurement is made
determining which digits are significant
all non-zero digits
eg. 1245 (4 significant figures)
2.3 (2 significant figures)
all captive zeros (zeros between non-zero digits)
2021 (4 significant figures)
5000.1 (5 significant figures)
leading zeros are never significant
0.0012 (2 significant figures) → placeholders
zeros at the end of a number (trailing zeros) are
not significant if there is no decimal point in the number:
230 (2 significant figures)
7000 (1 significant figure)
significant if there is a decimal point in the number
3.230 (4 significant figures)
7.0 (2 significant figures)
scientific notation
used to describe very large or very small numbers because
it’s time-consuming to read/write
easy to lose track of zeros and mess up
numbers are expressed with
one digit to the left of the decimal, multiplied by a power of ten
eg. 4.59x10^5
4.59 is the significand, 10 is the base, and 5 is the exponent.
if x > 1, the exponent is positive, and if x < 1, the exponent is negative
scientific notation and significant figures
significand determines number of significant figures
eg. 4.590 x 10^5 => 5 sigfigs (4.590)
significant figures in calculations
addition/subtraction—answer is rounded to the smallest significant decimal place
multiplication/division—answer is rounded to the number of digits that corresponds with the least number of significant figures in any of the numbers used in the calculation
dimensional analysis
used to convert a measurement from one unit to another using conversion factors
conversion factor: a ratio of equivalent measures (numerator = denominator)
when a measurement is multiplied by a conversion factor, the expression of measurement changes (because the units change) but the actual quantity measured remains the same