1.4. Measurement and Recording Data http://www.ck12.org
a. 0.191
b. 0.190
c. 00.19
d. 10.90
e. 10.060
f. 010.060Answers:
a. 3
b. 3
c. 2
d. 4
e. 5
f. 5Ambiguous Recording
How many significant digits are there for the number 100? We have a problem with this. As it is written, we
don’t know whether the zeros are placeholders or if the tool used to measure 100 can actually measure to the tens
place. Had the number been written as “100.” (with a decimal point after the third digit), then we could say, yes,
and we would know the measurement has three significant digits, with the ones-place being an estimate. But we
don’t typically write a number terminating in a decimal point. The best method for writing significant digits is using
scientific notation.
Let us restate the definition of scientific notation. Scientific notation expresses a measurement as a number between
1 and 10, then multiplied by a power of ten.
Some examples:
- 5,400 (2 significant figures) = 5.4× 103
- 5,400 (3 significant figures) = 5.40× 103
- 5,400 (4 significant figures) = 5.400× 103
- 0.0200 (3 significant figures) = 2.00× 10 −^2
If we had intended three significant digits for 100, we would have written it as 1.00× 102 , using scientific notation.
Had we intended one significant digit then we would have written it as 1× 102 using scientific notation.
Check Your Understanding
- Using scientific notation, write 2800 with four significant figures.
Answer: 2.800× 103.
- Using scientific notation write 28,000 with three significant figures.
Answer:2.80× 104.
Computing with Significant Digits
There are set rules used to determine the number of significant digits (or figures or numbers!) to report when adding,
subtracting, multiplying, and dividing with significant numbers. Let’s consider these rules.