Question

using this method, it is possible to solve many problems by using to another. for example, 12 inches = one foot. since these two same value, the fractions 12 in/1 ft and 1 ft/12 in are both equal multiply another number by the number one, you do not change may change its unit.
example 1: convert 2 miles to inches.
2 miles × 5,280 ft/1 mile × 12 inches/1 ft = 126,720 in (using signific 2 mi = 100,00
example 2: how many seconds are in 4 days?
4 days × 24 hrs/1 day × 60 min/1 hr × 60 sec/1 min = 345,600 (using sig 4 days =
solve the following problems. write the answers in significant

1. 3 hrs = ______ sec
2. 0.035 mg = ______ cg
3. 5.5 kg = ______ lbs
4. 2.5 yds = ______ in
5. 1.3 yrs = ______ hr (1 yr = 365 days)
6. 3 moles = ______ molecules (1 mole = 6.02 × 10²³ mole
7. 2.6 × 10²⁴ molecules = ______ moles
8. 5 moles = ______ liters (1 mole = 22.4 liters)
9. 100. liters = ______ moles

Explanation:

Step1: Convert hours to seconds

We know that 1 hour = 60 minutes and 1 minute = 60 seconds. So, 1 hour = \(60\times60 = 3600\) seconds.
For 3 hours, we multiply 3 by 3600: \(3\times3600=10800\) seconds.

Step2: Convert milligrams to centigrams

Since 1 centigram = 10 milligrams, to convert 0.035 mg to cg, we divide by 10: \(0.035\div10 = 0.0035\) cg.

Step3: Convert kilograms to pounds

We know that 1 kg ≈ 2.20462 lbs.
For 5.5 kg, we multiply 5.5 by 2.20462: \(5.5\times2.20462 = 12.12541\approx12.1\) lbs (using significant figures).

Step4: Convert yards to inches

Since 1 yard = 36 inches.
For 2.5 yds, we multiply 2.5 by 36: \(2.5\times36=90\) inches.

Step5: Convert years to hours

First, convert years to days: 1.3 yrs × 365 days/yr = 474.5 days.
Then convert days to hours: 474.5 days × 24 hrs/day = 11388 hours.

Step6: Convert moles to molecules

Given 1 mole = \(6.02\times10^{23}\) molecules.
For 3 moles, we multiply 3 by \(6.02\times10^{23}\): \(3\times6.02\times10^{23}=1.806\times10^{24}\) molecules.

Step7: Convert molecules to moles

If we have \(2.6\times10^{24}\) molecules, and 1 mole = \(6.02\times10^{23}\) molecules.
We divide by \(6.02\times10^{23}\): \(\frac{2.6\times10^{24}}{6.02\times10^{23}}\approx4.32\) moles.

Step8: Convert moles to liters

Given 1 mole = 22.4 liters.
For 5 moles, we multiply 5 by 22.4: \(5\times22.4 = 112\) liters.

Step9: Convert liters to moles

If we have 100 liters, and 1 mole = 22.4 liters.
We divide by 22.4: \(\frac{100}{22.4}\approx4.46\) moles.

Answer:

1. \(10800\)
2. \(0.0035\)
3. \(12.1\)
4. \(90\)
5. \(11388\)
6. \(1.806\times10^{24}\)
7. \(4.32\)
8. \(112\)
9. \(4.46\)