2. Metrics
Page 1
Metric System Basics
Introduction to the fundamental concepts of the metric system.
Page 2
The Metric System Overview
The metric system is structured around base units corresponding to specific measurements:
Length: Meter (m)
Volume: Liter (L)
Mass: Gram (g)
The combination of prefixes with base units forms the foundational elements of the metric system.
Example of Prefixes:
Centi + meter = Centimeter (cm)
Kilo + liter = Kiloliter (kL)
Page 3
Common Prefixes in Metric
The main prefixes used in the metric system include:
kilo (10^3)
hecto (10^2)
deca (10^1)
Base Units:
meter (m)
gram (g)
liter (L)
Sub-prefixes:
deci (10^-1)
centi (10^-2)
milli (10^-3)
Page 4
Measuring Length in Metric
Common examples of measuring length in metric units:
Length of a tree branch: 1.5 meters (m)
Length of a room: 5 meters (m)
Length of a ball of twine stretched out: 25 meters (m)
Page 5
Measuring Longer Distances
To represent longer distances more conveniently:
Distance from home to school: Approximately 16093 meters (m)
Conversion to kilometers: 16093 meters = 16.093 kilometers (km)
Rounded: 16.1 kilometers (km)
Page 6
Understanding Metric Prefixes and Powers of 10
Prefixes in the metric system relate to powers of 10, indicating scale changes:
Each prefix shift represents a change of either:
10 times larger or 10 times smaller.
Example:
Centimeters are 10 times larger than millimeters.
Conversion: 1 centimeter = 10 millimeters.
Page 7
Visualizing Lengths
Comparison of Measurements:
Centimeters are 10 times larger than millimeters, highlighting the relationship in length measurement.
Visual representation:
1 cm = 10 mm (Example not to scale with dimensional relation illustrated).
Page 8
Conversion Steps in Metric System
Movement within the metric system:
To convert between units:
Each step in the conversion process is equivalent to multiplying or dividing by 10.
Example Conversion Chain:
From base unit to centi:
1 liter = 10 deciliters = 100 centiliters.
2 grams = 20 decigrams = 200 centigrams.
Page 9
Simplifying Conversions
Moving Decimal Points:
The conversion can be simplified by adjusting the decimal point:
Example:
1 meter = 100 centimeters (1.00 meter = 100. centimeters).
Page 10
Conversion Practice
Convert the following:
20 grams (g) = ___ milligrams (mg).
Page 11
Step-by-Step Conversion Example
From meters to kilometers:
16093 meters = 1609.3 decameters = 160.93 hectometers = 16.093 kilometers.
Each step to kilo moves the decimal place one to the left.
Page 12
Decimal Movement Directions
Directionality in Decimals:
Moving to the left in the metric diagram means moving the decimal to the left.
Moving to the right means moving the decimal to the right.
Page 13
Another Conversion Practice
Convert:
20 centimeters (cm) = ___ meters (m).
Page 14
Converting Centimeters to Kilometers
Example:
400,000 centimeters = 4 kilometers (4.00000 km).
Page 15
Converting Meters to Kilometers
Example:
4000 meters = 4 kilometers.
Convert from centimeters to meters:
4000 centimeters = 40 meters.
Page 16
Additional Conversions
Conversions of lengths:
From meters to centimeters: 5 meters = 500 centimeters.
From kilometers to meters: 0.3 kilometers = 300 meters.
Page 17
Conversions to Smaller Units
Complex Conversions from kilometers:
4 kilometers = 4000000 millimeters.
Via other unit conversions:
4 kilometers = 40 hectometers = 400 decameters = 4000 meters = 40000 decimeters = 400000 centimeters = 4000000 millimeters.
Page 18
Summary of Metric System
Key Points:
Base units in the metric system are meter (m), liter (L), gram (g).
The metric system relies on powers of 10.
Conversions shift the decimal one place to the right or left.
Page 19
Final Conversion Practice
Convert the following amounts:
500 milliliters = ___ liters.
2 kilograms = ___ grams.
5.5 decagrams = ___ grams.
0.6 deciliters = ___ liters.
10 kilometers = ___ centimeters.
1 cubic centimeter (cm³) = volume equivalence in cubic millimeters (mm³).