Question

try these conversions, using the ladder method. * = dimensional analysis

1. 2000 mg = ___ g

• 2) 104 km = ___ m

1. 480 cm = ___ m

• 4) 5.6 kg = ___ g

1. 8 mm = ___ cm
2. 5 l = ___ ml
3. 198 g = ___ kg
4. 75 ml = ___ l
5. 50 cm = ___ m
6. 5.6 m = ___ cm

• 11) 16 cm = ___ mm

1. 2500 m = ___ km
2. 65 g = ___ mg

• 14) 6.3 cm = ___ mm

1. 120 mg = ___ g

Explanation:

Step1: Recall conversion factors

1 g = 1000 mg, 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 L = 1000 mL, 1 kg = 1000 g

Step2: Solve 1)

$2000\ mg=\frac{2000}{1000}g = 2g$

Step3: Solve 2)

$104\ km=104\times1000m = 104000m$

Step4: Solve 3)

$480\ cm=\frac{480}{100}m = 4.8m$

Step5: Solve 4)

$5.6\ kg=5.6\times1000g = 5600g$

Step6: Solve 5)

$8\ mm=\frac{8}{10}cm = 0.8cm$

Step7: Solve 6)

$5\ L=5\times1000mL = 5000mL$

Step8: Solve 7)

$198\ g=\frac{198}{1000}kg = 0.198kg$

Step9: Solve 8)

$75\ mL=\frac{75}{1000}L = 0.075L$

Step10: Solve 9)

$50\ cm=\frac{50}{100}m = 0.5m$

Step11: Solve 10)

$5.6\ m=5.6\times100cm = 560cm$

Step12: Solve 11)

$16\ cm=16\times10mm = 160mm$

Step13: Solve 12)

$2500\ m=\frac{2500}{1000}km = 2.5km$

Step14: Solve 13)

$65\ g=65\times1000mg = 65000mg$

Step15: Solve 14)

$6.3\ cm=6.3\times10mm = 63mm$

Step16: Solve 15)

$120\ mg=\frac{120}{1000}g = 0.12g$

Answer:

1. 2 g
2. 104000 m
3. 4.8 m
4. 5600 g
5. 0.8 cm
6. 5000 mL
7. 0.198 kg
8. 0.075 L
9. 0.5 m
10. 560 cm
11. 160 mm
12. 2.5 km
13. 65000 mg
14. 63 mm
15. 0.12 g