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4.5678. 600. 0.5008. Significant Figures. 1.004. 8. 9.99999. 32.000. 7. 2.45. Measurement always involves some estimating. The more accurate a measurement is, the closer it is to the true value.

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4.5678

600

0.5008

Significant Figures

1.004

8

9.99999

32.000

7

2.45


Measurement always involves some estimating.

The more accurate a measurement is, the closer it is to the truevalue.

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.

3.2

3

estimated

certain



1. All non-zero digits are significant.

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

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

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

3. Leading zeroes are NOTsignificant.

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


Always LOOK FOR A DECIMAL

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)


To avoid confusion, scientists commonly use SCIENTIFIC NOTATION.

ALL digits in scientific notation are SIGNIFICANT

6.02 x 10 23

  • Move the decimal so it is behind the first

  • non-zero digit.

  • 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 15 000

6.35 x 10 -4 0.000635

  • 103,000

  • 1,236,000

  • 42.0

  • 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


Rounding Rules

0-4: round down

5 -9: round up

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


Rules

for

Addition and Subtraction

Multiplication and Division


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.

  • Roundthe answer to match the value with the LEASTnumber of decimal places.

12.0 + 131.59 + 0.2798 = 143.8698

Answer = 143.9

least number of decimal places


  • Multiply or divide

  • Answer isrounded 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


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