Metric Conversions
Problems #1 - 10

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Here are the problems:

1. 750 micrograms to g6. 45.6 microliters to megaliters
2. 0.25 megameters to cm    7. 1.08 kg to μg
3. 23.8 fg to kg8. 9.57 x 10¯8 mm to nanometers
4. 2.77 kg to mg9. 2.00 L to mL
5. 2.90 cm to terameters10. 35.28 mL to L

Problem #1: Convert 750 μg to g:

750 μg x (_____ g / _____ μg) = _____ g

750 μg x (1 g / _____ μg) = _____ g <--- put "1" in front of larger unit

750 μg x (1 g / 106 μg) = _____ g <--- 106 μg in 1 g

Answer = 7.5 x 10-4 g <--- note negative exponent from 106 being in the denominator


Problem #2: Convert 0.25 Mm to cm:

0.25 Mm x (_____ cm / _____ Mm) = _____ cm <--- note capital M for mega

0.25 Mm x (_____ cm / 1 Mm) = _____ cm <--- a "1" in front of the larger unit

0.25 Mm x (108 cm / 1 Mm) = _____ cm <--- 108 cm in one megameter

Answer = 2.5 x 107 cm

In 2009, this problem was asked and answered on Yahoo Answers.


Problem #3: Convert 23.8 fg to kg


Problem #4: Convert 2.77 kg to mg

2.77 kg x (_____ mg / _____ kg) = _____ mg

2.77 kg x (_____ mg / 1 kg) = _____ mg <--- put "1" in front of larger unit

2.77 kg x (106 mg / 1 kg) = _____ mg <--- 6 is the exponent on the distance from kilo- (103) to milli- (10-3)

Answer = 2.77 x 106 mg


Problem #5: Convert 2.90 cm to terameters

2.90 cm x (_____ Tm / _____ cm) = _____ Tm

2.90 cm x (1 Tm / _____ cm) = _____ Tm

2.90 cm x (1 Tm / 1014 cm) = _____ Tm <--- tera- = 1012; centi- = 10-2

Answer = 2.90 x 10-14 Tm


Problem #6: Convert 45.6 microliters to megaliters


Problem #7: Convert 1.08 kg to μg

1.08 kg x (_____ μg / _____ kg) = _____ μg

1.08 kg x (_____ μg / 1 kg) = _____ μg

1.08 kg x (109 μg / 1 kg) = _____ μg <--- micro- = 10-6; kilo- = 103

Answer = 1.08 x 109 μg


Problem #8: Convert 9.57 x 10-8 mm to nanometers

9.57 x 10-8 mm x (_____ nm / _____ mm) = _____ mm

9.57 x 10-8 mm x (_____ nm / 1 mm) = _____ mm <--- milli- (at 10-3) is larger than nm (at 10-9)

9.57 x 10-8 mm x (106 nm / 1 mm) = _____ mm

Answer = 9.57 x 10-2 nm


Problem #9: Convert 2.00 L to mL

2.00 L x (1000 mL / L) = 2.00 x 103

Note that there is no 1 in front of the L. This is often done, where the 1 is understood to be there. Note the manner of the answer; it is done that way to show three significant figures.


Problem #10: Convert 35.28 mL to L

35.28 mL x (1 L / 1000 mL) = 0.03528 L

Note that, when the 1 is in the numerator, it is usually written.