1. Look up the equ iva lent va lues of the un its. 2 . Wr ite th is equa l it y as a f ract ion in order to simpl i f y the or ig ina l un it . In th is case, we want to simpl i f y nm. Therefore, we w r ite it as the denominator. 3. Mu lt iply the number of the or ig ina l un it by the conversion factor. Then simpl i f y the un its. Wr ite the resu lt in scient i f ic notat ion. 5.4. Converting units We a lso use a conversion factor to change one un it into another un it. To w r ite 0.27 nm in metres, fol low these steps: 23 A long jumper reaches the take-off board at a speed of 8.34 m/s. What is this speed in km/h? 24 The density of the air in a room is 1 225 in SI units. What are these units? Write the density in g/L. A C T I V I T I E S 1 nm = 10-9 m nm m 1 10 9 - Th is f ract ion is the conversion factor. . . ? ? m m nm nm 0 27 1 10 0 27 10 9 9 = - - 0.27 nm = 2 .7 ? 10-10 m To cha nge der ived u n it s , we ca n u se mu lt iple conversion fa ctors one a f ter the other. Look at these examples. S O LV E D P R O B L E M 4 The radius of an atom is 0.85 nm. Write this in m. ? ? ? 8.5 10 m . . nm m m 0 85 1 10 0 85 10 nm 10 9 9 = = - - - S O LV E D P R O B L E M 5 A film lasts for 2 hours. Write this in seconds. 1 h = 3 600 s ? 2 h 1 h 3 600 s 7200 s = Conversion factor Conversion factor 1 nm = 10-9 m S O LV E D P R O B L E M 6 The speed of a car is 90 km/h. Write this in m/s. 1 km = 1 000 m 1 h = 3 600 s ? ? 1 10 3 600 1 90 h km km m s h 25 s m 3 = S O LV E D P R O B L E M 7 The density of seawater is 1.13 g/mL. Write this in International System (SI) units. 1 kg = 1 000 g 1 mL = 10-6 m3 ? ? ? . . . kg m m m kg 1 13 10 1 10 1 1 13 10 1 13 10 mL g g mL kg 3 3 3 3 6 3 3 = = - - 1 23
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