Question

metric system conversion lab
today, we will be using the metric system
units of measurement that we have been learning
about in class to take different measurements of
different objects. after we perform our
measurements, we will convert to other units that are within the metric system (i.e
centimeters to kilometers). you and your partner(s) will need to complete the foll
tables. note: these measurements do not need to be done in order, but eac
needs to be filled in completely by the end. your ladder is shown below.
kilo- hecto- deka- base unit length deci- centi-

object	kilometers (km)	meters (m)	centimeters (cm)	millim (m
2. table width				6
3. table height				2
4. length of back counter				5
5. physical science book length
6. physical science book width
7. physical science book height
8. your height
9. length of square table in commons
10. width of classroom door

(top right: conversion ladder with kilo, hecto, deca, meter, etc., labeled bigger units with ×10 arrows)

Explanation:

To solve metric system conversions (e.g., converting meters to kilometers or centimeters), we use the metric prefix relationships. The metric system is based on powers of 10, where each prefix represents a power of 10 relative to the base unit (meter for length).

General Conversion Rule:

To convert between units, we use the relationship between the prefixes. For example:

• \( 1 \text{ kilometer (km)} = 1000 \text{ meters (m)} \) (or \( 1 \text{ m} = 10^{-3} \text{ km} \))
• \( 1 \text{ meter (m)} = 100 \text{ centimeters (cm)} \) (or \( 1 \text{ cm} = 10^{-2} \text{ m} \))

Example: Converting Table Length (1.1 m) to Kilometers and Centimeters

Let’s use the table length (1.1 m) as an example.

Step 1: Convert Meters to Kilometers

We know \( 1 \text{ km} = 1000 \text{ m} \), so to convert meters to kilometers, divide by 1000 (or multiply by \( 10^{-3} \)):
\[
1.1 \text{ m} \times \frac{1 \text{ km}}{1000 \text{ m}} = 1.1 \times 10^{-3} \text{ km} = 0.0011 \text{ km}
\]

Step 2: Convert Meters to Centimeters

We know \( 1 \text{ m} = 100 \text{ cm} \), so to convert meters to centimeters, multiply by 100:
\[
1.1 \text{ m} \times \frac{100 \text{ cm}}{1 \text{ m}} = 110 \text{ cm}
\]

Applying to Other Objects

For any object, follow these steps:

1. Identify the base unit (e.g., meters from the table).
2. Choose the target unit (e.g., kilometers, centimeters, millimeters).
3. Use the metric prefix relationship (e.g., \( 1 \text{ m} = 10^3 \text{ mm} \), \( 1 \text{ km} = 10^6 \text{ mm} \), etc.) to set up the conversion factor.
4. Multiply/divide to convert the unit.

Example for a Physical Science Book (e.g., length = 0.25 m)

• To kilometers: \( 0.25 \text{ m} \times 10^{-3} = 0.00025 \text{ km} \)
• To centimeters: \( 0.25 \text{ m} \times 100 = 25 \text{ cm} \)
• To millimeters: \( 0.25 \text{ m} \times 1000 = 250 \text{ mm} \)

Key Takeaway

The metric system uses powers of 10 for conversions, so converting between units involves multiplying or dividing by 10 (or powers of 10) based on the prefixes. Use the ladder method (or prefix relationships) to determine the number of places to move the decimal.

If you need help with a specific object or conversion, provide the measured value (in meters, for example), and we can walk through the calculation!

Answer:

To solve metric system conversions (e.g., converting meters to kilometers or centimeters), we use the metric prefix relationships. The metric system is based on powers of 10, where each prefix represents a power of 10 relative to the base unit (meter for length).

General Conversion Rule:

To convert between units, we use the relationship between the prefixes. For example:

• \( 1 \text{ kilometer (km)} = 1000 \text{ meters (m)} \) (or \( 1 \text{ m} = 10^{-3} \text{ km} \))
• \( 1 \text{ meter (m)} = 100 \text{ centimeters (cm)} \) (or \( 1 \text{ cm} = 10^{-2} \text{ m} \))

Example: Converting Table Length (1.1 m) to Kilometers and Centimeters

Let’s use the table length (1.1 m) as an example.

Step 1: Convert Meters to Kilometers

We know \( 1 \text{ km} = 1000 \text{ m} \), so to convert meters to kilometers, divide by 1000 (or multiply by \( 10^{-3} \)):
\[
1.1 \text{ m} \times \frac{1 \text{ km}}{1000 \text{ m}} = 1.1 \times 10^{-3} \text{ km} = 0.0011 \text{ km}
\]

Step 2: Convert Meters to Centimeters

We know \( 1 \text{ m} = 100 \text{ cm} \), so to convert meters to centimeters, multiply by 100:
\[
1.1 \text{ m} \times \frac{100 \text{ cm}}{1 \text{ m}} = 110 \text{ cm}
\]

Applying to Other Objects

For any object, follow these steps:

1. Identify the base unit (e.g., meters from the table).
2. Choose the target unit (e.g., kilometers, centimeters, millimeters).
3. Use the metric prefix relationship (e.g., \( 1 \text{ m} = 10^3 \text{ mm} \), \( 1 \text{ km} = 10^6 \text{ mm} \), etc.) to set up the conversion factor.
4. Multiply/divide to convert the unit.

Example for a Physical Science Book (e.g., length = 0.25 m)

• To kilometers: \( 0.25 \text{ m} \times 10^{-3} = 0.00025 \text{ km} \)
• To centimeters: \( 0.25 \text{ m} \times 100 = 25 \text{ cm} \)
• To millimeters: \( 0.25 \text{ m} \times 1000 = 250 \text{ mm} \)

Key Takeaway

The metric system uses powers of 10 for conversions, so converting between units involves multiplying or dividing by 10 (or powers of 10) based on the prefixes. Use the ladder method (or prefix relationships) to determine the number of places to move the decimal.

If you need help with a specific object or conversion, provide the measured value (in meters, for example), and we can walk through the calculation!