Significant Figures

Significant Figures Significant Figures Notes – Physical

Science 1. Significant figures apply to measured

values. They are significant to the measurement NOT to the number.

2. The number of significant figures is determined by the resolution of the instrument used to make the measurement.

The last digit in a measured number is always the “estimated” digit.

Rules for Counting Significant Figures

Non-zero numbers are ALWAYS significant.

Example: 312cm and 0.546mm both have ______ significant figures3

Sig. Fig. Rules - continued

Leading Zeros are NEVER significant. Example: 0.000047pm has _____

significant figures. consider this number in scientific

notation:4.7 x 10-5

How many significant figures?

2

Sig. Fig. Rules - continued

Captured Zeros , zeros between two non zero numbers, are ALWAYS significant.

Example: Both 4,005km and 40.05dm contain ______ significant figures.

4

Sig. Fig. Rules - continued

Trailing Zeros are only significant if they are present with a decimal place.

Example: 120mL has _____ sig. figs. 120.0mL has _____ sig. figs.

Which number was measured with the more accurate volumetric measuring device?

2

4

Sig. Fig. Rules - continued

Significant figures DO NOT APPLY to “counted” or “exact” numbers or definitions.

Examples: 1 inch = 2.54 cm has NO sig. Fig. 14 pencils has NO sig figs.

You do not use these numbers to determine the number of sig figs in your answer

Significant Figures Rules Summary

Non-zero numbers – Always Significant

Captured zeros – Always Significant

Leading zeros – Never Significant

Trailing zeros – Only with a decimal

Counted numbers – does not apply

Numeric Definitions – does not apply

Rounding Rules Rule 1 - if the remainder beyond the

last digit to be reported is less than 5, drop the numbers past the last digit.

Example: Rounding to one decimal place, the number 5.3467 becomes 5.3.

Rule 2 - if the remainder is equal or greater than 5, increase the final digit by 1.

Example: The number 5.798 becomes 5.8 if rounding to 2 digits. 4.025 becomes 4.03 if rounding to 3 digits.

Multiplying/Dividing with Significant Figures:

The answer will have the same number of sig figs as the number with the least sig. figs in the calculation.

Example: 30 x 5.1 = _______BUT: 30 has only ____ sig fig so the answer can only have _____ sig fig.

The correct answer is _____

153

11

200

Adding/Subtracting with Significant Figures The answer will have the same number

of decimal places as the number with the least decimal places in the calculation.

Example: 331.34 + 3.2 = ___________

BUT 3.2 has only one decimal place so the rounded answer is ______

334.54

334.5

Practice – How many significant

figures?

46 marbles 3.02 x 102 cm 0.003407 in. 230 mL 2.4cm x 3.21cm 5.66mL + 1.234mL 6.02 x 1023 atoms

None3

4223

None