 # Significant Digits. Why are they important? -Show precision of instruments used -We use them ALL THE TIME in Chemistry -MUST KNOW THE RULES!!

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Significant Digits

Why are they important? -Show precision of instruments used -We use them ALL THE TIME in Chemistry -MUST KNOW THE RULES!!

1. Digits other than zero are always significant 96 g.2 significant digits 61.42 g.4 significant digits 0.538 g.3 significant digits

2. One or more trailing zeros after the decimal point are always significant 4.00000 s.6 significant digits 0.05600 s.4 significant digits 0.002 m.1 significant digits

3. Zeros between two other significant digits are always significant 5.029 km.4 significant digits 30600 km.3 significant digits 0.050060 km.5 significant digits

4. A zero can be made significant by placing a bar over it. We normally write these in scientific notation, but here are some examples _ 10 mL2 significant digits _ 1000 mL4 significant digits _ 100000 mL3 significant digits

An exception to the rules.. When talking about a value that is absolute, all digits are significant. 25 apples2 significant digits 10 planes2 significant digits 800 students3 significant digits

Strategy to determine number of significant digits 1. Find the leftmost significant digit (leftmost nonzero digit) 2. Find your rightmost significant digit (rightmost nonzero digit, a zero after a decimal, or a zero with a bar over it) 3. All digits in between are significant

Practice! 1. 70.12 L8. -270.8 K 2. 0.000800 mg.9. 1000 mL 3. 82.003 mm.10. 42,729.00 cm 4. 27.0 km11. 225 beans 5. 50 people12. 99.294 dm 6. 1.002 cm13. 0.06900 m _ _ 7. 200kg14. 3200000 kL

Using Significant Digits for Calculations Multiplying and Dividing 1. look at original numbers 2. determine number with least amount of significant digits 3. answer should contain this amount of significant digits

Example When multiplying 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm 3. 22.37 shows 4 significant digits 3.10 shows 3 significant digits 85.75 shows 4 significant digits Answer would have only 3 significant digits: 5950 cm^3.

Practice 1. 24 mm x 31.8 mm = 2. 8.40 g / 4.2 mL = 3. 200 dm x 3.58 dm = 4. 5500 km / 55.0 s =

Adding and Subtracting 1. Look at original numbers 2. Find the one with least number of decimal places 3. Answer should contain this amount of decimal places

Example When we add: 3.76 g + 14.83 g + 2.1 g = 20.69 g 3.76 g2 decimal places 14.83 g2 decimal places 2.1 g1 decimal place Final answer should have one decimal place: 20.7

Practice 1. 49.1 g + 8.001 g = 2. 81.350 m - 7.35 m = 3. 4.60 s + 3 s = 4. 67.5 cm - 0.009 cm =

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