Typically, scientific notation is used for this purpose. If 200 has two significant figures, then 2.0
x 10
2
is used. If it has three, then 2.00 x 10
2
is used. If it had four, then 200.0 is sufficient. See
rule #2 above.
How will you know how many significant figures are in a number like 200? In a problem like
below, divorced of all scientific context, you will be told. If you were doing an experiment, the
context of the experiment and its measuring devices would tell you how many significant figures
to report to people who read the report of your work.
Zero Type #4: leading zeros in a whole number.
00250 has two significant figures. 005.00 x 10¯
4
has three.
Exact Numbers
Exact numbers, such as the number of people in a room, have an infinite number of significant
figures. Exact numbers are counting up how many of something are present, they are not
measurements made with instruments. Another example of this are defined numbers, such as 1
foot = 12 inches. There are exactly 12 inches in one foot. Therefore, if a number is exact, it
DOES NOT affect the accuracy of a calculation nor the precision of the expression. Some more
examples:
There are 100 years in a century.
2 molecules of hydrogen react with 1 molecule of oxygen to form 2 molecules of water.
There are 500 sheets of paper in one ream.
Interestingly, the speed of light is now a defined quantity. By definition, the value is 299,792,458
meters per second.
Are Significant Figures Important? A Fable
A student once needed a cube of metal that had to have a mass of 83 grams. He knew the density
of this metal was 8.67 g/mL, which told him the cube's volume. Believing significant figures
were invented just to make life difficult for chemistry students and had no practical use in the
real world, he calculated the volume of the cube as 9.573 mL. He thus determined that the edge
of the cube had to be 2.097 cm. He took his plans to the machine shop where his friend had the
same type of work done the previous year. The shop foreman said, "Yes, we can make this
according to your specifications - but it will be expensive."
"That's OK," replied the student. "It's important." He knew his friend has paid $35, and he had
been given $50 out of the school's research budget to get the job done.
He returned the next day, expecting the job to be done. "Sorry," said the foreman. "We're still
working on it. Try next week." Finally the day came, and our friend got his cube. It looked very,
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