Question

1. what is a standard of measurement?
2. how can you distinguish between which multiples of a unit? and give 2 examples
3. how can related si units be converted?
4. put the following measurements in order from smallest to largest: kilometer, micrometer, nanometer, centimeter, meter
5. why is density a derived unit?
6. make the following conversions: a. 27 degrees celsius to kelvin b. 2g to kg c. 500 m to km
7. what is the density of an unknown metal that has a mass of 158 g and a volume of 20 ml? be sure to label the answer with a unit.

start date 08/28/2025 12:00
end date 08/29/2025 10:28
score release date 08/30/2025 6:00
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score 0
total points 2

Answer:

1. What is a standard of measurement?

• Brief Explanation: A standard of measurement is a precisely - defined and reproducible quantity used as a reference for measuring physical quantities. For example, the meter is a standard for length, defined based on the distance light travels in a certain fraction of a second. It allows for consistent and accurate communication of measurements across different locations and times.
• Answer: A precisely - defined and reproducible quantity used as a reference for measuring physical quantities.

1. How can you distinguish between which multiples of a unit?

• Brief Explanation: Multiples of a unit are distinguished by prefixes. For example, kilo - means 1000 times the base unit, centi - means 1/100 of the base unit, and milli - means 1/1000 of the base unit. These prefixes clearly indicate the relationship of the multiple to the base unit.
• Answer: By using prefixes that indicate the relationship to the base unit (e.g., kilo -, centi -, milli -).

1. How can related SI units be converted?

• Brief Explanation: SI units can be converted using conversion factors based on the relationships between the base and derived units. For example, to convert between length units like meters and kilometers, use the factor 1 km = 1000 m. Multiply or divide by the appropriate factor depending on the direction of conversion.
• Answer: Use conversion factors based on the relationships between base and derived units.

1. Put the following measurements in order from smallest to largest: Kilometer, micrometer, nanometer, centimeter, meter

• Explanation:
• Step 1: Recall the size relationships of the prefixes
• Nano - is \(10^{-9}\), micro - is \(10^{- 6}\), centi - is \(10^{-2}\), and kilo - is \(10^{3}\) times the base unit (meter).
• Step 2: Order the units
• Nanometer (\(10^{-9}\) m) < Micrometer (\(10^{-6}\) m) < Centimeter (\(10^{-2}\) m) < Meter (1 m) < Kilometer (\(10^{3}\) m)
• Answer: Nanometer, micrometer, centimeter, meter, kilometer.

1. Why is density a derived unit?

• Brief Explanation: Density is defined as mass per unit volume. Mass and volume are base or fundamental quantities with their own units (e.g., kilograms for mass and cubic meters for volume). Since density is calculated as the ratio of two different fundamental quantities, it is a derived unit.
• Answer: Because it is defined as the ratio of mass (a fundamental quantity) to volume (a fundamental quantity).

1. Make the following conversions: a. 27 degrees Celsius to Kelvin; b. 2g to kg; c. 500 m to km

• Explanation:
• a. Convert 27 degrees Celsius to Kelvin
• Step 1: Use the conversion formula
• The formula to convert Celsius to Kelvin is \(K = ^{\circ}C+ 273.15\).
• Substitute \(^{\circ}C = 27\) into the formula: \(K=27 + 273.15=300.15\) K.
• b. Convert 2g to kg
• Step 1: Recall the conversion factor
• Since \(1\ kg = 1000\ g\), then \(1\ g=\frac{1}{1000}\ kg\).
• To convert 2g to kg, multiply 2 by \(\frac{1}{1000}\): \(2\ g=2\times\frac{1}{1000}\ kg = 0.002\ kg\).
• c. Convert 500 m to km
• Step 1: Recall the conversion factor
• Since \(1\ km = 1000\ m\), then \(1\ m=\frac{1}{1000}\ km\).
• To convert 500 m to km, multiply 500 by \(\frac{1}{1000}\): \(500\ m=500\times\frac{1}{1000}\ km = 0.5\ km\).
• Answer:
• a. 300.15 K
• b. 0.002 kg
• c. 0.5 km

1. What is the density of an unknown metal that has a mass of 158 g and a volume of 20 mL?

• Explanation:
• Step 1: Recall the density formula
• The density formula is \(

ho=\frac{m}{V}\), where \(
ho\) is density, \(m\) is mass, and \(V\) is volume.

• Step 2: Convert units if necessary
• Here, we can use the given units directly since \(1\ mL = 1\ cm^{3}\).
• Substitute \(m = 158\ g\) and \(V = 20\ cm^{3}\) into the formula: \(

ho=\frac{158\ g}{20\ cm^{3}}=7.9\ g/cm^{3}\)

• Answer: \(7.9\ g/cm^{3}\)