# Significant Figures and Conversion of Units

1. A fisherman catches two striped bass. The smaller of the two has a measured length of 93.46 cm(two decimal places, four significant figures), and the larger fish has a measured length of 135.3cm (one decimal place, four significant figures). What is the total length of fish caught for the day?

2. How many significant figures are there in (a) 78.9 + 0.2, (b) 3.788 X 10^9, (c) 2.46 X 10^-6, (d) 0.003^2.

3. The radius of a circle is measured to be (10.5 + 0.2) m. Calculate (a) the area and (b) the circumference of the circle, and give the uncertainty in each value.

4. Carry out the following arithmetic operations: (a) the sum of the measured of the values 756, 37.2, 0.83, and 2.5; (b) the product 0.003^2 X 356.3; (c) the product 5.620 X Pie

5. A fathom is a unit of length, usually reserved for measuring the depth of water. A fathom is approximately 6 ft in length. Take the distance from Earth to the Moon to be 250 000 miles, and use the given approximation to find the distance to fathoms.

6. Suppose your hair grows at the rate of 1/32 inch per day. Find the rate at which it grows in nanometers per second. Because the distance between atoms in a molecule is on the order of 0.1 nm.

7. A house is 50.0 ft long and 26 ft wide and has 8.0-ft-high ceilings. What is the volume of the interior of the house in cubic meters and in cubic meters and in cubic centimeters?

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#### Solution Summary

This solution is comprised of detailed explanation and step-by-step calculation of the given problems and provides students with a clear perspective of the underlying concepts.

Chemistry: Unit Conversion and Significant Figures

1. Write each of the following as standard numbers.

1.2×104s

8.25×10−2kg

4×106g

5×10−3m

2. How many significant figures are in each of the following measurements?

20.60 L

200.66 g

4.00 m

18.4 ∘C

780 060 000 g

3. Round off each of the following measurements to three significant figures.

1.854 kg

163.4476 L

0.004 738 265 cm

7996 m

4. Perform each of the following calculations, and give answers with the correct number of decimal places:

41.74cm + 4.893cm

23.90g + 104.4g+0.015g

169.080mL− 21.0mL

1.14L− 0.630L

5. Perform each of the following calculations and give answers with the correct number of significant figures:

300×190

2.80/(4)(135)

0.819×3.4×5.7

5.3×0.252/5.86×30.0

6. Use metric conversion factors to solve the following problems.

- The height of a student is 173 cm. How tall is the student in meters?

- A cooler has a volume of 5500 mL . What is the capacity of the cooler in liters?

- A hummingbird has a mass of 0.0059 kg . What is the mass of the hummingbird in grams?