Sig. Figs.Sig. Figs.

Essential Questions:Essential Questions:

What are sig. figs?What are sig. figs?How are they used in science?How are they used in science?

What rules are used to govern sig. What rules are used to govern sig. figs. when doing calculations?figs. when doing calculations?

What are Sig. Figs?What are Sig. Figs? They are those digits that carry They are those digits that carry

meaning contributing to a meaning contributing to a measurement or value’s accuracy. measurement or value’s accuracy.

Sig. Figs. is short for “significant Sig. Figs. is short for “significant figures or digits.”figures or digits.”

The RulesThe Rules to follow when identifying to follow when identifying which digits are significant.which digits are significant.

1.1. ALL non-zero numbers are always ALL non-zero numbers are always significant. Ex. 1, 234 cm or significant. Ex. 1, 234 cm or 5.225 g5.225 g

2.2. Zeros between non-zero numbers Zeros between non-zero numbers are always significant. Ex. 2, 008 m are always significant. Ex. 2, 008 m

3.3. Zeros to theZeros to the left left are never are never significant. Ex. 0.0052 significant. Ex. 0.0052 kg (You only count the 5 and 2 as kg (You only count the 5 and 2 as significant.)significant.)

The RulesThe Rules cont. cont.

44. . Zeros to the Zeros to the rightright of a non-zero number of a non-zero number when a decimalwhen a decimal is involved are is involved are significant. Ex. 3050. mL significant. Ex. 3050. mL (The decimal makes the last zero (The decimal makes the last zero significant.) or 0.45000 g (The three zeros significant.) or 0.45000 g (The three zeros after the five are significant, while the zero after the five are significant, while the zero to the left is not.)to the left is not.)

25,000 g (Only the 2 and 5 are significant, 25,000 g (Only the 2 and 5 are significant, because there is NO decimal present!)because there is NO decimal present!)

55. . All Exact values are significant, even if All Exact values are significant, even if they contain zeros. Ex. 1,760 yds = 1.0 they contain zeros. Ex. 1,760 yds = 1.0 miles 60 s = 1 min.miles 60 s = 1 min.

Try some…Try some… Determine the number of sig. figs. in Determine the number of sig. figs. in

each value.each value.

1.1.300,500 g300,500 g

2.2.10.004500 m10.004500 m

3.3.1,234,567.890 mL1,234,567.890 mL

4.4.100 cm100 cm

5.5.250. hg250. hg

The AnswersThe Answers……1. 4 (The zeros after the 5 do not count, 1. 4 (The zeros after the 5 do not count,

because no decimal is present. The because no decimal is present. The first two zeros are counted, because first two zeros are counted, because they are in-between non-zero numbers.)they are in-between non-zero numbers.)

2. 8 (All of the digits are significant.)2. 8 (All of the digits are significant.)

3. 10 (All digits are significant.)3. 10 (All digits are significant.)

4. 1 (Only the 1 is significant, because 4. 1 (Only the 1 is significant, because there is no decimal to include the there is no decimal to include the zeros.)zeros.)

5. 3 (All the digits are significant; there is 5. 3 (All the digits are significant; there is a decimal.)a decimal.)

Rules to follow for calculations:Rules to follow for calculations:

When adding and subtracting, the When adding and subtracting, the number of sig. figs. is based on number of sig. figs. is based on decimal placement. The original value decimal placement. The original value with the fewest decimal places is the with the fewest decimal places is the value that must be used for the final value that must be used for the final answer. (Normal rounding rules answer. (Normal rounding rules apply…5 or greater: round up; 4 or apply…5 or greater: round up; 4 or lower: round down)lower: round down)

Ex. 12.35 g + 1.345 g = 13.695 g ~ 13.70 Ex. 12.35 g + 1.345 g = 13.695 g ~ 13.70 gg(2 dec.) (3 dec.) (3 dec.) (F.A. = 2 dec)(2 dec.) (3 dec.) (3 dec.) (F.A. = 2 dec)

Rules for MathRules for Math (cont.) (cont.)

When multiplying and dividing, the When multiplying and dividing, the answer must have the same number answer must have the same number of sig. figs. as the original number of sig. figs. as the original number with the least sig. figs. The key is to with the least sig. figs. The key is to do the math, and then round at the do the math, and then round at the end to the correct sig. figs.end to the correct sig. figs.

Ex. 5.0 cm x 5 cm = 25.0 cmEx. 5.0 cm x 5 cm = 25.0 cm2 2 ~ 30 ~ 30 cmcm22