Significant figures

The number of digits which describe a measurement

Measurements

Rules for significant figures

• All nonzero numbers are significant

• All zeros between significant digits are significant

• All numbers BOTH after a significant digit AND after a DECIMAL are significant.

• Placeholders are never significant

1, 2, 3, 4….. 9 ex: 34521 = five significant figures

ex: 30001 = five significant figures

ex: 3.0000 = five significant figures

ex: 0.00010 = two significant figures

Your turn

• 12 000• 0.000 3• 23.000• 24• 999.000• 0.000 10• 56.0• 44.3

• 12.000• 0.000 300• 23.000 1• 0.002 4• 9 909.000• 0.001 000• 506.0• 0044.3

• 1 200.0• 0.030 000• 2 003 000• 204• 999 000• 0.000 00 10• 005 6.0• 4 004.3

Counting numbers – have infinite significant figures, as do conversion

facctors which are definitions.• 0.001 km is EXACTLY 1/1000• 100 cm is exactly 100• 3 basketballs cannot be 3.1 basketballs.

Rules for adding

• Anything which lines up can be added.• 100 + 200 = 300• 110 + 200 still equals 300 because 200 has only

one significant digit, so the zero is being added to an unknown number. (200 could be 160 or it could be 240 because it only has one significant digit.)

• 1.00 + 2.2222 = 3.22 because there is nothing in the 1/1000 place of the 1.00 so we don’t know SHOULD be there. 1.00 could be 0.995 or it could be 1.004 and would still be written as 1.00.

100200300

110200300

We don’t know whatthe tens’ place reallyis!

Rules for subtracting• Anything which lines up can be

subtracted.• 300 - 200 = 100• 310 - 200 still equals 100 because

200 has only one significant digit, So we don’t know if it is 200 or 210 or 220 or even 249.

• 3.00 - 2.2222 = 1.88 because there is nothing in the 1/1000 place of 3.00 so we don’t know SHOULD be there.

Rules for multiplication and division

• Whichever number has the fewest significant digits determines the number of significant digits in the answer.

• 11.1 x 2.0 = 22.2, but it must be rounded to 22 because 2.0 has only two significant digits.

• 11.111 x 2.00 = 22.222, but it must be rounded to 22.2 because 2.00 has only three significant digits.

• 33.333/1.0 = 33 because 1.0 has only two significant figures.