Problems #1 - 10

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Here are the problems:

1. 750 micrograms to g 6. 45.6 microliters to megaliters 2. 0.25 megameters to cm 7. 1.08 kg to μg 3. 23.8 fg to kg 8. 9.57 x 10¯ ^{8}mm to nanometers4. 2.77 kg to mg 9. 2.00 L to mL 5. 2.90 cm to terameters 10. 35.28 mL to L

**Problem #1:** Convert 750 μg to g:

750 μg x (_____ g / _____ μg) = _____ g750 μg x (1 g / _____ μg) = _____ g <--- put "1" in front of larger unit

750 μg x (1 g / 10

^{6}μg) = _____ g <--- 10^{6}μg in 1 g

Answer = 7.5 x 10^{-4} g <--- note negative exponent from 10^{6} being in the denominator

**Problem #2:** Convert 0.25 Mm to cm:

0.25 Mm x (_____ cm / _____ Mm) = _____ cm <--- note capital M for mega0.25 Mm x (_____ cm / 1 Mm) = _____ cm <--- a "1" in front of the larger unit

0.25 Mm x (10

^{8}cm / 1 Mm) = _____ cm <--- 10^{8}cm in one megameterAnswer = 2.5 x 10

^{7}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) = _____ mg2.77 kg x (_____ mg / 1 kg) = _____ mg <--- put "1" in front of larger unit

2.77 kg x (10

^{6}mg / 1 kg) = _____ mg <--- 6 is the exponent on the distance from kilo- (10^{3}) to milli- (10^{-3})

Answer = 2.77 x 10^{6} mg

**Problem #5:** Convert 2.90 cm to terameters

2.90 cm x (_____ Tm / _____ cm) = _____ Tm2.90 cm x (1 Tm / _____ cm) = _____ Tm

2.90 cm x (1 Tm / 10

^{14}cm) = _____ Tm <--- tera- = 10^{12}; 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) = _____ μg1.08 kg x (_____ μg / 1 kg) = _____ μg

1.08 kg x (10

^{9}μg / 1 kg) = _____ μg <--- micro- = 10^{-6}; kilo- = 10^{3}

Answer = 1.08 x 10^{9} μg

**Problem #8:** Convert 9.57 x 10^{-8} mm to nanometers

9.57 x 10^{-8}mm x (_____ nm / _____ mm) = _____ mm9.57 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 (10^{6}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 10^{3}

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.