Question

dimensional analysis problems
convert the following problems. show all your work! box your final answer.

1. how many liters are there in 2.444 e14 nanoliters?

1. how many meters are there in 1.45 e-12 centimeters?

1. how many grams are there in 1.77 e 9 micrograms?

1. how many milliliters are there in 0.440 liters?

1. how many decaliters are there in 47 liters?

1. how many meters are there in 97 centimeters?

1. how many hectograms are there in 0.235 grams?

1. how many inches are there in 45.6 cm?

1. how many centimeters are there in 1.23 e-6 kilometers?

Explanation:

Problem 1:

Step1: Recall the conversion factor: 1 liter = \(10^9\) nanoliters. So to convert nanoliters to liters, divide by \(10^9\).

Given \(2.444\times10^{14}\) nanoliters. The conversion formula is: Liters = Nanoliters \(\times\frac{1}{10^9}\)

Step2: Substitute the value and calculate.

Liters = \(2.444\times10^{14}\times\frac{1}{10^9}\) = \(2.444\times10^{14 - 9}\) = \(2.444\times10^{5}\) = 244400

Step1: Recall the conversion factor: 1 meter = 100 centimeters (or 1 centimeter = \(10^{-2}\) meters). So to convert centimeters to meters, multiply by \(10^{-2}\).

Given \(1.45\times10^{-12}\) centimeters. The conversion formula is: Meters = Centimeters \(\times10^{-2}\)

Step2: Substitute the value and calculate.

Meters = \(1.45\times10^{-12}\times10^{-2}\) = \(1.45\times10^{-12 - 2}\) = \(1.45\times10^{-14}\)

Step1: Recall the conversion factor: 1 gram = \(10^6\) micrograms (or 1 microgram = \(10^{-6}\) grams). So to convert micrograms to grams, multiply by \(10^{-6}\).

Given \(1.77\times10^{9}\) micrograms. The conversion formula is: Grams = Micrograms \(\times10^{-6}\)

Step2: Substitute the value and calculate.

Grams = \(1.77\times10^{9}\times10^{-6}\) = \(1.77\times10^{9 - 6}\) = \(1.77\times10^{3}\) = 1770

Answer:

\(\boxed{244400}\)

Problem 2: