SI units are built from seven base units, including meters for length, kilograms for mass, and seconds for time. Derived units combine base units, such as for force and for energy. Metric prefixes show powers of ten, so and .
Unit conversion works best when you multiply by conversion factors equal to .
Key Facts
- The SI base unit for length is the meter, written as .
- The SI base unit for mass is the kilogram, written as , not the gram.
- The SI base unit for time is the second, written as .
- Force is measured in newtons, and .
- Energy and work are measured in joules, and .
- Power is measured in watts, and .
- Common metric prefixes include , , , , and .
- To convert units, multiply by a fraction equal to , such as .
Vocabulary
- SI system
- The international measurement system used in science, based on standard units such as , , and .
- Base unit
- A fundamental SI unit that is not made from other units, such as the meter or second .
- Derived unit
- A unit made by combining base units, such as the newton or joule .
- Metric prefix
- A symbol added before a unit to show a power of ten, such as for or for .
- Conversion factor
- A ratio equal to that changes a measurement from one unit to another without changing its value.
- Dimensional analysis
- A method for checking or converting units by tracking how units cancel in a calculation.
Common Mistakes to Avoid
- Confusing for meters with as a prefix is wrong because the same letter can mean different things depending on position. In , the first means milli and the second means meter.
- Using grams as the SI base unit for mass is wrong because the SI base unit is . Many derived units, such as , require mass in kilograms.
- Moving the decimal the wrong direction during prefix conversions is wrong because prefixes represent powers of ten. For example, , so kilometers convert to a larger number of meters.
- Dropping squared or cubed units during conversions is wrong because area and volume conversions must square or cube the conversion factor. For example, , not .
- Writing unit symbols with plural letters or periods is wrong because SI symbols do not take plurals or periods. Use , not or .
Practice Questions
- 1 Convert to meters.
- 2 Convert to seconds.
- 3 Show that the unit of force from is when mass is in and acceleration is in .
- 4 Explain why unit cancellation helps you decide whether a physics calculation is set up correctly.
Understanding SI Units & Metric Prefixes
Units do more than label a number. They tell you what kind of measurement the number represents. A speed of twenty has no useful meaning until its unit is known.
Twenty meters per second describes a fast bicycle or car. Twenty kilometers per hour is much slower. In physics, units act like a built in error check.
When calculating a quantity, the units must combine into the kind of unit expected for the answer. If a calculation for speed ends with seconds times meters, something has gone wrong.
This method is called dimensional analysis. It helps students catch errors before comparing a result with an answer key.
Conversions become especially important when measurements contain squared or cubed lengths. Area depends on length times length, so a change in length unit is applied twice. One square meter contains ten thousand square centimeters, not one hundred square centimeters.
Volume depends on length times length times length. One cubic meter contains one million cubic centimeters. This is a common source of mistakes in density, pressure, and volume problems.
Write the unit next to every number at each step. Then convert the complete unit carefully instead of converting only the number.
Scientific notation keeps extremely large and small measurements readable. It is useful for distances in space, sizes of cells, electric charge, and the mass of tiny particles. A number written in scientific notation has one nonzero digit before the decimal point, followed by a power of ten.
The exponent shows how far the decimal point would move. A positive exponent represents a large value. A negative exponent represents a small value.
Metric prefixes are a quick spoken and written form of some powers of ten. Still, scientific notation is often clearer during multistep calculations because exponents can be tracked directly.
Careful unit use matters outside school. Medicine labels use milligrams and milliliters. Running apps may switch between kilometers and miles.
Household electricity is billed in kilowatt hours, which is an energy unit rather than a power unit. Lab instruments may report micrometers, nanometers, or megapascals. Pay close attention to capital letters because symbols can have different meanings.
A lowercase m means meter, while an uppercase M can represent the prefix mega in a unit name. Keep units through every line of work, round only near the end, and check whether the size of the final answer makes sense in the real situation.