Question

determine whether the measurements are greater than (>), less than (<), or equal to (=).

1. 3 km > 2000 m
2. 5 cm = 50 mm
3. 7 g > 500 cg
4. 30 mm = 3 cm
5. 40 cm < 4 m
6. 536 ml < 53.6 dl
7. 300 m < 3 km
8. 6 cm < 80 mm
9. 800 cg > 7 g
10. 5 km > 4900 m
11. 3.6 l > 36 cl
12. complete the following table by indicating the most appropriate unit for expressing that measurement. then tell whether that unit is a derived unit, a base unit, or a base unit modified by a prefix.

measurement	unit	derived, base, or modified
b. area of sioux falls	kilometer
c. mass of a fingernail	centigram
d. area of a bacterial colony	millimeter

1. you calculate the volume of a box to be 437 cm³. the actual volume of the box is 445 cm³. what is your percent error?

%e = \frac{|a - e|}{a}×100
e = \frac{|445 - 437|}{445}×100 1.80%

Explanation:

Step1: Convert units for comparison

1 km = 1000 m, 1 cm = 10 mm, 1 g = 100 cg, 1 L = 100 cL, 1 dL = 100 mL.

Step2: Analyze each comparison

• 22. 3 km = 3×1000 m = 3000 m, so 3 km > 2000 m.
• 23. 5 cm = 5×10 mm = 50 mm, so 5 cm = 50 mm.
• 24. 7 g = 7×100 cg = 700 cg, so 7 g > 500 cg.
• 25. 30 mm = 30÷10 cm = 3 cm, so 30 mm = 3 cm.
• 26. 4 m = 4×100 cm = 400 cm, so 40 cm < 4 m.
• 27. 53.6 dL = 53.6×100 mL = 5360 mL, so 536 mL < 53.6 dL.
• 28. 3 km = 3×1000 m = 3000 m, so 300 m < 3 km.
• 29. 6 cm = 6×10 mm = 60 mm, so 6 cm < 80 mm.
• 30. 800 cg = 800÷100 g = 8 g, so 800 cg > 7 g.
• 31. 5 km = 5×1000 m = 5000 m, so 5 km > 4900 m.
• 32. 3.6 L = 3.6×100 cL = 360 cL, so 3.6 L > 36 cL.

Step3: Complete the table

• a. Mass of an elephant: kilogram, base - unit modified by prefix.
• b. Area of Sioux Falls: square - kilometer (should be area unit, not kilometer), derived unit.
• c. Mass of a fingernail: milligram (centigram is not the best - centigram is relatively large for a fingernail), base - unit modified by prefix.
• d. Area of a bacterial colony: square - millimeter (should be area unit, not millimeter), derived unit.

Step4: Calculate percent error

The percent - error formula is $\%e=\frac{|a - e|}{a}\times100$, where $a$ is the actual value and $e$ is the experimental value. Here, $a = 445$ cm³ and $e = 437$ cm³.
$\%e=\frac{|445 - 437|}{445}\times100=\frac{8}{445}\times100\approx1.80\%$

Answer:

1. >
2. =
3. >
4. =
5. <
6. <
7. <
8. <
9. >
10. >
11. >
12. a. kilogram, base - unit modified by prefix; b. square - kilometer, derived unit; c. milligram, base - unit modified by prefix; d. square - millimeter, derived unit
13. 1.80%