Significant Figures Handout

The Five (5) Basic Rules of Determining Significant Figures 1.

In measurements with all non-zero digits, all digits are always significant. 24.7 g has 3 s.f. 21.256 has 5 s.f. 2. All zeros located between non-zero digits are always significant. 2.02 has 3 s.f. 0.9009 mm has 4 s.f. 3. Zeros located in front of non-zero digits are placeholders. They are never significant. 0.0009 has 1 s.f. 0.00423 has 3 s.f. 0.00607 has 3 s.f. 4. Zeros located after the last non-zero digit and to the right of the decimal point are always significant – they communicate the level of precision in the instrument. 0.280 has 3 s.f. 430.000 has 6 s.f. 0.8000 has 4 s.f. 5. Zeros at the end of the measurement and to the left of the decimal point are very confusing. They are not significant if they are just placeholders. 300 m and 7000 m each have just 1 s.f., and 27,210 has only 4 s.f. However, if the 300 m measurement was taken with a meter stick marked to the nearest meter, then it really should be reported as 300.0 m. To avoid ambiguity, we would report this measurement in scientific notation as 3.000 x 102 m. That way we know the measurement has 4 s.f. and not just 1 s.f.

The Five (5) Basic Rules of Determining Significant Figures 1. In measurements with all non-zero digits, all digits are always significant. 2. 3. 4. 5.

24.7 g has 3 s.f. 21.256 has 5 s.f. All zeros located between non-zero digits are always significant. 2.02 has 3 s.f. 0.9009 mm has 4 s.f. Zeros located in front of non-zero digits are placeholders. They are never significant. 0.0009 has 1 s.f. 0.00423 has 3 s.f. 0.00607 has 3 s.f. Zeros located after the last non-zero digit and to the right of the decimal point are always significant – they communicate the level of precision in the instrument. 0.280 has 3 s.f. 430.000 has 6 s.f. 0.8000 has 4 s.f. Zeros at the end of the measurement and to the left of the decimal point are very confusing. They are not significant if they are just placeholders. 300 m and 7000 m each have just 1 s.f., and 27,210 has only 4 s.f. However, if the 300 m measurement was taken with a meter stick marked to the nearest meter, then it really should be reported as 300.0 m. To avoid ambiguity, we would report this measurement in scientific notation as 3.000 x 102 m. That way we know the measurement has 4 s.f. and not just 1 s.f.

The Five (5) Basic Rules of Determining Significant Figures 1. In measurements with all non-zero digits, all digits are always significant. 24.7 g has 3 s.f.

21.256 has 5 s.f.

2. All zeros located between non-zero digits are always significant. 2.02 has 3 s.f.

0.9009 mm has 4 s.f.

3. Zeros located in front of non-zero digits are placeholders. They are never significant. 0.0009 has 1 s.f. 0.00423 has 3 s.f. 0.00607 has 3 s.f. 4. Zeros located after the last non-zero digit and to the right of the decimal point are always significant – they communicate the level of precision in the instrument. 0.280 has 3 s.f. 430.000 has 6 s.f. 0.8000 has 4 s.f. 5. Zeros at the end of the measurement and to the left of the decimal point are very confusing. They are not significant if they are just placeholders. 300 m and 7000 m each have just 1 s.f., and 27,210 has only 4 s.f. However, if the 300 m measurement was taken with a meter stick marked to the nearest meter, then it really should be reported as 300.0 m. To avoid ambiguity, we would report this measurement in scientific notation as 3.000 x 102 m. That way we know the measurement has 4 s.f. and not just 1 s.f.