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Chapter 1: Problem 44

a. How many kilograms are in 1 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 1 milliliter? f. How many picograms are in 1 microgram?

Short Answer

Expert verified
a. \(10^9\) kg b. \(6.50 \times 10^{23}\) nm c. \(25 \times 10^{-18}\) kg d. 8.0 L e. \(10^3\) µL f. \(10^3\) pg

Step by step solution

01

a. How many kilograms are in 1 teragram?

To convert from teragrams (Tg) to kilograms (kg), we need to know the conversion factor between the two. One teragram is equal to \(10^{12}\) grams, and since there are 1000 grams in a kilogram, we have to multiply by \(10^9\). 1 Tg = \(1 \times 10^9\) kg So, there are \(10^9\) kilograms in 1 teragram.
02

b. How many nanometers are in 6.50 × 10² terameters?

To convert from terameters (Tm) to nanometers (nm), we need to know the conversion factor between the two. One terameter is equal to \(10^{12}\) meters, and since there are \(10^9\) nanometers in a meter, we have to multiply by \(10^{21}\). 6.50 × 10² Tm = 6.50 × 10² × 10²¹ nm = 6.50 × 10²³ nm So, there are 6.50 × 10²³ nanometers in \(6.50 \times 10^2\) terameters.
03

c. How many kilograms are in 25 femtograms?

To convert from femtograms (fg) to kilograms (kg), we need to know the conversion factor between the two. One femtogram is equal to \(10^{-15}\) grams, and since there are 1000 grams in a kilogram, we have to divide by \(10^{18}\). 25 fg = 25 × 10⁻¹⁸ kg So, there are \(25 \times 10^{-18}\) kilograms in 25 femtograms.
04

d. How many liters are in 8.0 cubic decimeters?

To convert from cubic decimeters (dm³) to liters (L), we need to know that one cubic decimeter is equal to one liter. Therefore, the conversion factor is 1. 8.0 dm³ = 8.0 L So, there are 8.0 liters in 8.0 cubic decimeters.
05

e. How many microliters are in 1 milliliter?

To convert from milliliters (mL) to microliters (µL), we need to know the conversion factor between the two. One milliliter is equal to \(10^3\) microliters. 1 mL = \(1 \times 10^3\) µL So, there are \(10^3\) microliters in 1 milliliter.
06

f. How many picograms are in 1 microgram?

To convert from micrograms (µg) to picograms (pg), we need to know the conversion factor between the two. One microgram is equal to \(10^3\) picograms. 1 µg = \(1 \times 10^3\) pg So, there are \(10^3\) picograms in 1 microgram.

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