Significant Figures1.004

4.5678

32.000

600

2.45

0.5008

7

9.99999

8

Measurement always involves some estimating.

A better instrument allows for better measurements, recorded as a greater number of significant figures (digits).

Recording - include EVERY digit that is absolutely certain...PLUS the ONE digit that is estimated.

These are the SIGNIFICANT FIGURES.

3.2certainestimated

3

Rules for Significant Figures

2. All zeroes between non-zero digits are significant.

50407 (5 sig figs) 8.001 (4 sig figs)

1. All non-zero digits are significant.

374 (3 sig figs) 8.1 (2 sig figs)

3. Leading zeroes are NOT significant.

0.54 (2 sig figs) 0.0098 (2 sig figs)

4. Trailing zeroes are significant ONLY if there is a decimal point.

2370 (3 sig figs) 16000 (2 sig figs)

160.0 (4 sig figs) 000.1800 (4 sig figs)

Always LOOK FOR A DECIMAL

To avoid confusion, scientists commonly use SCIENTIFIC NOTATION.

ALL digits in scientific notation are SIGNIFICANT

6.02 x 10 23

1. Move the decimal so it is behind the first non-zero digit.

2. Count the number of places that you moved the

decimal - to the left is +, right is -

238000 2.38 x 10 5

0.0052 5.2 x 10 -3

1.5 x 10 4 15 0006.35 x 10 -4 0.000635

1. 103,0002. 1,236,000 3. 42.0 4. 0.00000021 5. 0.000238

1.03 x 10 5

1.236 x 10 6

4.20 x 10 1

2.1 x 10 -7

2.38 x 10 -4

0-4: round down5 -9: round up

Rounding Rules

0.00533 (2 sig figs) 0.0053

426.3 (3 sig figs) 426

1890 (1 sig fig) 2000

0.0296 (2 sig figs) 0.030

Addition and Subtraction

Multiplication and Division

Rulesfor

You can only give an answer that is as accurate as your least accurate number.

Add or subtract

• Count digits to the right of the decimal.

• Round the answer to match the value with the LEAST number of decimal places.

Answer = 143.9least number of decimal places

12.0 + 131.59 + 0.2798 = 143.8698

Multiply or divide

• Answer is rounded to contain the same number of sig figs as the value with the LEAST.

51.3 × 13.75 = 705.375

The answer, with significant figures, is 705.

DO NOT round for each calculation.

When performing multiple calculations, use the rule of the final calculation to round the answer.

(0.3012 + 0.2)(3.6) = ?

(0.5)(3.6) = 1.8= 2

(0.5012)(3.6) = 1.80432 = 1.8