SIGNIFICANT DIGITS IN MEASURED AND EXACT QUANTITIES

1. Indicate whether each of the following is a measured or an exact quantity. 5 books exact 12 roses exact 5 lb measured 16 ounces in one pound exact 9.25 g measured 361 miles measured 0.035 kg measured 1000 m in 1 km exact

2. State the number of significant figures in each of the following quantities. 6.5 g 2 s.f. 300.0 L 4 s.f. 0.018 g 2 s.f. 3.9800×1010 atoms 5 s.f. 0.00608 g 3.s.f. $2,546, 000 4 s.f. 1.360 mL 4 s.f. 655 million beans 3 s.f. 4.5 m 2 s.f. 204.25 g 5 s.f. 0.0004 L 1 s.f. 6.25×105 mm 3 s.f. 805 lb 3 s.f. 34.80 km 4 s.f. 2.50×10 – 3 L 3 s.f. 8×105 g 1 s.f. 1200 km 2 s.f. 250. mL 3 s.f. 1500 meter freestyle swimming 4 s.f.

SCIENTIFIC NOTATION

1. Perform the following mathematical operations without using a calculator. 102 × 105 = 107 10–24 × 105 = 10–19 1016 × 10–5 × 10–11 = 1

=4

2

1010 10–2 =−

−

6

3

1010 103 =−10

5

1010 1015 =

−

18

4

1010 10–22

2. Write the following numbers in scientific notation. 93 million 9.3×107 760000000 (3 sig. figs.) 7.60×108 0.0001206 1.206×10–4 0.00000450 4.50×10–6 0.00130 1.30×10–3 0.055×1010 5.5×108 4,450,000 (4 sig. figs.) 4.450×106 0.00032 3.2×10–4 38,000 3.8×104 25.2 2.52×101 0.0000000021 2.1×10–9 0.0505 5.05×10–2

3. Write the following numbers in scientific notation. 0.0102×10–3 1.02×10–5 1.9912×10–5 1.9912×10–5 4551×104 4.551×107 0.08178×10–3 8.178×10–5 6022×1020 6.022×1023 27.21×10–4 2.721×10–3

4. Write the following as standard decimal numbers. 4.09×102 409 3.00×10–4 0.000300 5.315×101 53.15 8.2×10–3 0.0082 3.150×103 3150. 2.46×10–6 0.00000246

METRIC PREFIXES

Fill the blanks in the table. The table must be memorized!

Prefix kilo- deci- centi- milli- micro- nano- pico-

Symbol k d c m μ n p

10n 103 10‒1 10‒2 10‒3 10‒6 10‒9 10‒12

1. Do the following unit conversions by moving the decimal point.

123 cm = 1.23 m 134000 m = 134 km 50 mg = 0.05 g 0.0000000206 g = 0.0206 μg 12 mL = 0.012 L 3600 J = 3.6 kJ

2. Do the following unit conversions by changing power of 10. Write the final result either in decimal or in scientific notation which ever seems to be most appropriate in terms of presentation of the final result.

2.98×10−5 g = 29.8 μg 7.82×108 g = 7.82×105 kg 265 nm = 2.65×10−7 m 536 μL = 0.536 mL 4.365×10−10 cm = 4.365×10−3 nm 1.33×10−3 nm = 1.33 pm 8.209×10−6 km = 0.08209 dm

3. Draw one square centimeter broken into square millimeters. How many mm3 in one cm3? 1 cm2 = 100 mm2

Approximately how many feet are in one meter? 3. Now imagine one m2 (a square with one meter sides). Approximately how many square feet are in one square meter? [Hint: On the back of this sheet sketch (scaled down) a drawing of one square meter broken into square feet.]

1 m2 ≈ 9 ft2

How many mm3 are in one cm3? 1000. How many cm3 are in one m3? 106 . 4. Do the following unit conversions by changing power of 10. Write the final result either in decimal or in

scientific notation which ever seems to be the most appropriate in terms of presentation of the final result.

569 cm3 = 0.569 dm3 0.078 pm2 = 7.8×10−20 mm2 7.09×1015 cm3 = 7.09×1027 μm3 3.67×10−19 mm3 = 0.367 nm3

135600 dm2 = 0.001356 km2 1.35×10−9 cm3 = 1.35×10−9 mL

Answer Key

SCIENTIFIC NOTATION AND METRIC PREFIXES 1. Express each number in scientific notation.

0.009080 = 9.080×10─3 0.003950×103 = 3.950×100 450×10─10 (3 s.f.) = 4.50×10─8 6230000 (3 s.f.) = 6.23×106 0.0302×105 = 3.02×103 46 = 4.6×101 2.5 = 2.5×100 0.054×10─4 = 5.4×10─6

2. Complete the table by performing unit conversions. Use scientific notation for numbers that have more than three leading or tailing placeholder zeros. Write the numbers with units.

mm cm dm km

3.20×106 mm 3.20×105 cm 3.20×104 dm 3.20 km

6.9×10─2 dm 6.9×10─3 dm 6.9×10─4 dm 6.9×10─8 km

0.405 mm 0.0405 cm 0.00405 dm 4.05×10─7 km

3. Complete the table by performing unit conversions. Use scientific notation for numbers that have more

than three leading or tailing placeholder zeros. Write the numbers with units.

m3 dm3 L cm3 mL

3.20×102 m3 3.20×105 dm3 3.20×105 L 3.20×108 cm3 3.20×108 mL

6.9×10─14 m3 6.9×10─11 dm3 6.9×10─11 L 6.9×10─8 cm3 6.9×10─8 mL

6.01×10─6 m3 0.00601dm3 0.00601 L 6.01 cm3 6.01 mL