# Download To determine the number of significant figures in a measurement

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```
In a measurement,
◦ All of the digits known with certainty and one
“uncertain” or estimated digit

Related to the precision of the measuring
instrument
◦ The smallest divisions on the scale determine the
number of certain digits
◦ Estimate one place past the smallest division on the
scale
Rules
1. Non zero digits are significant
2. A zero is significant if it is
a.“terminating AND right” of the decimal [must be
both]
b.“sandwiched” between significant figures
c. Has a bar over it
3. Exact or counting numbers have an 
amount of significant figures as do constants
and conversion factors
Give the number of significant figures for each of
the following results.
a. A student’s extraction procedure on tea yields
0.0105 g of caffeine.
b. A chemist records a mass of 0.050080 g in an
analysis.
c. In an experiment, a span of time is determined
to be 8.050 × 10-3 s .

× and 
◦ The term with the least number of significant
figures determines the number of significant

4.56 × 1.4 = 6.38 = 6.4
limiting term

+ and (−)
◦ The term with the least number of decimal places
determines the number of significant figures in the
12.11
18.0  limiting term
+1.013
31.123= 31.1



pH – the number of significant figures in least
accurate measurement determines the
number of decimal places on the pH (and vice
versa).
[H+]=0.10M
2 significant figures
pH=-log[H+]=-log(0.10)= 1=1.00
2 decimal places

Round at the end of all calculations

Look at the significant figure one place beyond
your desired number of significant figures
◦ Carry AT LEAST one extra digit through intermediate
calculations
◦ Usually just look at the given data and round your final
answer to the least number of sig figs in data
◦ When in doubt, round to 3 sig figs 
◦ Scientific notation is your friend
◦ No points lost as long as you are within +/- one sig.
figure
◦ if >5 round up; <5 drop the digit.

Don’t “double round” !!
◦ 4.348 to 2 SF = 4.3 (NOT the 8 makes the 4 a 5 then the
5 makes the 3 a 4 =4.4)
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