Answered

Using this method, it is possible to solve many problems by using the relationship of one unit to another. For example, 12 inches [tex]\(= 1\)[/tex] foot. Since these two numbers represent the same value, the fractions [tex]\(\frac{12 \text{ in}}{1 \text{ ft}}\)[/tex] and [tex]\(\frac{1 \text{ ft}}{12 \text{ in}}\)[/tex] are both equal to one. When you multiply another number by the number one, you do not change its value; however, you may change its unit.

Example 2: How many seconds are in 4 days?
[tex]\[
4 \text{ days} \times \frac{24 \text{ hrs}}{1 \text{ day}} \times \frac{60 \text{ min}}{1 \text{ hr}} \times \frac{60 \text{ sec}}{1 \text{ min}} = 345,600 \text{ sec}
\][/tex]
(Using significant figures)
[tex]\[
4 \text{ days} = 300,000 \text{ sec}
\][/tex]

Solve the following problems. Write the answers in significant figures.

1. [tex]\(3 \text{ hrs} = \quad \text{ sec}\)[/tex]
2. [tex]\(0.035 \text{ mg} = \quad \text{ cg}\)[/tex]
3. [tex]\(5.5 \text{ kg} = \quad \text{ lbs}\)[/tex]
4. [tex]\(2.5 \text{ yds} = \quad \text{ in}\)[/tex]
5. [tex]\(1.3 \text{ yrs} = \quad \text{ hr} \quad (1 \text{ yr} = 365 \text{ days})\)[/tex]
6. [tex]\(3 \text{ moles} = \quad \text{ molecules} \quad (1 \text{ mole} = 0.02 \times 10^{25} \text{ molecules})\)[/tex]
7. [tex]\(2.5 \times 10^{21} \text{ molecules} = \quad \text{ moles}\)[/tex]
8. [tex]\(5 \text{ moles} = \quad \text{ liters} \quad (1 \text{ mole} = 22.4 \text{ liters})\)[/tex]
9. [tex]\(100 \text{ liters} = \quad \text{ moles}\)[/tex]
10. [tex]\(50 \text{ liters} = \quad \text{ molecules}\)[/tex]
11. [tex]\(5.0 \times 10^{25} \text{ molecules} = \quad \text{ liters}\)[/tex]
12. [tex]\(7.5 \times 10^3 \text{ mL} = \quad \text{ liters}\)[/tex]



Answer :

GinnyAnswer
Sure, let's solve each of the conversion problems step by step. We will use the provided relationships between different units to convert them.

1. Convert 3 hours to seconds:
[tex]\(3 \text{ hrs} = 3 \times 3600 \text{ sec/hr} = 10800 \text{ sec}\)[/tex]

2. Convert 0.035 mg to cg:
[tex]\(0.035 \text{ mg} = 0.035 \times 0.1 \text{ cg/mg} = 0.0035 \text{ cg}\)[/tex]

3. Convert 5.5 kg to lbs:
[tex]\(5.5 \text{ kg} = 5.5 \times 2.20462 \text{ lbs/kg} = 12.1254 \text{ lbs}\)[/tex]

4. Convert 2.5 yds to inches:
[tex]\(2.5 \text{ yds} = 2.5 \times 36 \text{ in/yd} = 90 \text{ in}\)[/tex]

5. Convert 1.3 years to hours (1 year = 365 days):
[tex]\(1.3 \text{ yrs} = 1.3 \times 365 \text{ days/yr} \times 24 \text{ hrs/day} = 11388 \text{ hrs}\)[/tex]

6. Convert 3 moles to molecules (1 mole = [tex]\(0.02 \times 10^{25}\)[/tex] molecules):
[tex]\(3 \text{ moles} = 3 \times 0.02 \times 10^{25} \text{ molecules/mole} = 6 \times 10^{23} \text{ molecules}\)[/tex]

7. Convert [tex]\(2.5 \times 10^{21}\)[/tex] molecules to moles:
[tex]\(2.5 \times 10^{21} \text{ molecules} / (0.02 \times 10^{25} \text{ molecules/mole}) = 0.0125 \text{ moles}\)[/tex]

8. Convert 5 moles to liters (1 mole = 22.4 liters):
[tex]\(5 \text{ moles} = 5 \times 22.4 \text{ liters/mole} = 112 \text{ liters}\)[/tex]

9. Convert 100 liters to moles:
[tex]\(100 \text{ liters} / 22.4 \text{ liters/mole} = 4.464285714 \text{ moles}\)[/tex]

10. Convert 50 liters to molecules:
[tex]\[ 50 \text{ liters} / 22.4 \text{ liters/mole} = 2.232143 \text{ moles} \][/tex]
[tex]\[ 2.232143 \times 0.02 \times 10^{25} \text{ molecules/mole} = 4.464285714 \times 10^{23} \text{ molecules} \][/tex]

11. Convert [tex]\(5.0 \times 10^{25}\)[/tex] molecules to liters:
[tex]\[ 5.0 \times 10^{25} \text{ molecules} / (0.02 \times 10^{25} \text{ molecules/mole}) = 2500 \text{ moles} \][/tex]
[tex]\[ 2500 \times 22.4 \text{ liters/mole} = 56000 \text{ liters} \][/tex]

12. Convert [tex]\(7.5 \times 10^3\)[/tex] mL to liters:
[tex]\[ 7.5 \times 10^3 \text{ mL} / 1000 \text{ mL/liter} = 7.5 \text{ liters} \][/tex]

The answers are:

1. [tex]\(3 \text{ hrs} = 10800 \text{ sec}\)[/tex]
2. [tex]\(0.035 \text{ mg} = 0.0035 \text{ cg}\)[/tex]
3. [tex]\(5.5 \text{ kg} = 12.1254 \text{ lbs}\)[/tex]
4. [tex]\(2.5 \text{ yds} = 90 \text{ in}\)[/tex]
5. [tex]\(1.3 \text{ yrs} = 11388 \text{ hrs}\)[/tex]
6. [tex]\(3 \text{ moles} = 6 \times 10^{23} \text{ molecules}\)[/tex]
7. [tex]\(2.5 \times 10^{21} \text{ molecules} = 0.0125 \text{ moles}\)[/tex]
8. [tex]\(5 \text{ moles} = 112 \text{ liters}\)[/tex]
9. [tex]\(100 \text{ liters} = 4.4643 \text{ moles}\)[/tex]
10. [tex]\(50 \text{ liters} = 4.4643 \times 10^{23} \text{ molecules}\)[/tex]
11. [tex]\(5.0 \times 10^{25} \text{ molecules} = 56000 \text{ liters}\)[/tex]
12. [tex]\(7.5 \times 10^3 \text{ mL} = 7.5 \text{ liters}\)[/tex]