Significant figures

convert measurement: 0.0390kg =____g.

39.0 g

# of sig figs: 0.01203 kg

4

# of sig figs: 1234

4

calculate using sig figs: 4.02 + 0.001=

4.02

convert measurement: 1.0cm =____m.

0.010 m

# of sig figs: 1000

1

# of sig figs: 200 L

1

convert measurement: 1.7m =____mm.

1,700 mm

rules

1. all nonzero digits, 2. zeros between nonzero digits, 3. final zeros to the right of the decimal place, 4. zeros that are place holders are not sig figs

calculate using sig figs: 123.4567cm - 1.23cm=

122.23 cm

calculate using sig figs: 123.4567cm - 22.00cm=

145.46 cm

round # to 3 sig figs: 23,456

23,500

round # to 3 sig figs: 234.45

234

round # to 3 sig figs: 234.56

235

calculate using sig figs: 123.4567cm x 2.00cm=

247 cm^2

# of sig figs: 0.00102

3

# of sig figs: 10200

3

# of sig figs: 103 mL

3

# of sig figs: 12.0 g

3

# of sig figs: 123 cm

3

# of sig figs: 0.0010200

5

# of sig figs: 0.023400 ft

5

# of sig figs: 10234

5

# of sig figs: 0.01023040

7

calculate using sig figs: 83.25 - 0.1075=

83.15

All non-zero digits are considered significant.

All non-zero digits are considered significant.

The number 0 has one significant figure. Therefore, any zeros after the decimal point are also significant. Example: 0.00 has....

Example: 0.00 has three significant figures.

When converting from decimal form to sci/nota, always maintain the same # of sig/figs. For ex., 0.00012 has _____ sig/figs, therefore the correct sci/nota for this number would be 1.2 x _______.

For ex., 0.00012 has two sig/figs, therefore the correct sci/nota for this number would be 1.2 x 10-4.

A bar may be placed over the last significant figure, showing that any trailing zeros following this are insignificant. For example, 1300 with a bar placed over the first 0 would have _____ sig/figs (the bar indicating that the # is precise to the nearest ten).

For ex., 1300 with a bar placed over the first 0 would have 3 sig/figs (the bar indicating that the # is precise to the nearest ten).

Any numbers in scientific notation are considered significant. For example, 4.300 x 10-4 has ____ sig/figs

For example, 4.300 x 10-4 has 4 significant figures.

_____________ zeros (zeros ___________ non-zero numbers) are not significant. For example, 0.00052 has two significant figures: 5 and 2.

Leading zeros (zeros before non-zero numbers) are not significant. For example, 0.00052 has two significant figures: 5 and 2.

If a measurement that is "Precise to four decimal Places" (0.0001) is given as 12.23, then the measurement might be understood as having only two decimal places of precision available. Stating the result as

Stating the result as 12.2300 makes it clear that the measurement is precise to four decimal places (in this case, six significant figures).

__________ zeros (zeros _________ non-zero numbers) in a number without a decimal are generally not significant

Trailing zeros (zeros after non-zero numbers) in a number without a decimal are generally not significant

_____________ zeros in a number containing a ___________ point are significant.

Trailing zeros in a number containing a decimal point are significant. example, 12.2300 has six sig/figs: 1, 2, 2, 3, 0, and 0. 0.000122300 has six sig/figs (the 0s before the 1 aren't sig/figs). 120.00 has five sig/figs since it has three trailing zeros.

The last sig/fig of a number may be underlined; for ex., "2000" has _____ sig/figs.

Two

significant figures

include all known digits plus one estimated digit

When adding and subtracting, the final # should be rounded to the decimal point of the ____________ precise number.

least 234.67 - 43.5 = 191.2 since 43.5 has one decimal place and 234.67 has two decimal places, the final answer must have just one decimal place.

Measured numbers have a _____________ number of significant figures.

limited

Exact numbers cannot be ____________ and have an ____________ __________ of significant figures.

simplified, infinite number

When multiplying and dividing numbers, the # of sig/figs used is determined by the original # with the _____________ amount of sig/figs.

smallest 1.423 x 4.2 = 6.0 since 1.423 has 4 significant figures and 4.2 only has two significant figures, the final answer must also have 2 significant figures

A decimal point may be placed after the #. For ex., "100." indicates specifically that ________ sig/figs are meant.

three

An exact number has absolutely no _________________ in it.

uncertainty