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Chapter 1: Problem 40

a. How many kilograms are in one teragram? b. How many nanometers are in \(6.50 \times 10^{2}\) terameters? c. How many kilograms are in 25 femtograms? d. How many liters are in \(8.0\) cubic decimeters? e. How many microliters are in one milliliter? f. How many picograms are in one microgram?

Short Answer

Expert verified
a. \(1 \times 10^9 \) kg b. \( 6.50 \times 10^{23} \) nm c. \( 2.5 \times 10^{-17} \) kg d. 8.0 liters e. 1000 µL f. 1000 pg

Step by step solution

01

a. Convert teragrams to kilograms

To convert from teragrams (Tg) to kilograms (kg), we need to know the conversion factor. 1 Tg equals 10^12 grams, and since there are 10^3 grams in a kilogram, we have: 1 Tg = 10^12 g = 10^12 / 10^3 kg = 10^9 kg So there are 10^9 kg in one teragram.
02

b. Convert terameters to nanometers

To convert from terameters (Tm) to nanometers (nm), first convert terameters to meters by multiplying by the conversion factor of 10^12, and then convert meters to nanometers by multiplying by the conversion factor of 10^9. Thus, we have: \( 6.50 \times 10^{2}\) Tm = \( 6.50 \times 10^{2} \times 10^{12} \) m = \( 6.50 \times 10^{14} \) m Now, convert meters to nanometers: \( 6.50 \times 10^{14} \) m = \( 6.50 \times 10^{14} \times 10^9 \) nm = \( 6.50 \times 10^{23} \) nm So there are \( 6.50 \times 10^{23} \) nanometers in \( 6.50 \times 10^{2} \) terameters.
03

c. Convert femtograms to kilograms

To convert from femtograms (fg) to kilograms (kg), first convert femtograms to grams by dividing by the conversion factor of 10^15, and then convert grams to kilograms by dividing by the conversion factor of 10^3. Thus, we have: 25 fg = 25 / 10^15 g = \( 2.5 \times 10^{-14} \) g Now, convert grams to kilograms: \( 2.5 \times 10^{-14} \) g = \( 2.5 \times 10^{-14} / 10^3 \) kg = \( 2.5 \times 10^{-17} \) kg So there are \( 2.5 \times 10^{-17} \) kg in 25 femtograms.
04

d. Convert cubic decimeters to liters

Since 1 cubic decimeter (dm³) is equal to 1 liter (L), we can simply write: 8.0 cubic decimeters = 8.0 liters
05

e. Convert milliliters to microliters

To convert from milliliters (mL) to microliters (µL), multiply by the conversion factor of 10^3. Thus, we have: 1 mL = 1 * 10^3 µL = 1000 µL So there are 1000 microliters in one milliliter.
06

f. Convert micrograms to picograms

To convert from micrograms (µg) to picograms (pg), multiply by the conversion factor of 10^3. Thus, we have: 1 µg = 1 * 10^3 pg = 1000 pg So there are 1000 picograms in one microgram.

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Most popular questions from this chapter

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