- Use metric prefixes to convert units and solve problems
- Convert between U.S. customary and metric units of length, weight/mass, and volume
- Convert between different temperature scales using conversion formulas
The Metric System
The metric system uses the base units meter, liter, and gram to measure length, liquid volume, and mass.The metric system is a base [latex]10[/latex] system. This means that each successive unit is [latex]10[/latex] times larger than the previous one.The names of metric units are formed by adding a prefix. to the basic unit of measurement. To tell how large or small a unit is, you look at the prefix. To tell whether the unit is measuring length, mass, or volume, you look at the base.
| kilo- | hecto- | deka- |
meter gram liter |
deci- | centi- | milli- |
| [latex]1,000[/latex] times larger than base unit | [latex]100[/latex] times larger than base unit | [latex]10[/latex] times larger than base unit | base units | [latex]10[/latex] times smaller than base unit | [latex]100[/latex] times smaller than base unit | [latex]1,000[/latex] times smaller than base unit |
You can view the transcript for “A beginners guide to the Metric System” here (opens in new window).
Converting Units Up and Down the Metric Scale
- K (king) for kilo- ([latex]1,000[/latex] times)
- H (henry) for hecto- ([latex]100[/latex] times)
- Da (died) for deca- ([latex]10[/latex] times)
- B (by) for base unit (meter, liter, gram, etc.)
- D (drinking) for deci- ([latex]0.1[/latex] times)
- C (chocolate) for centi- ([latex]0.01[/latex] times)
- M (milk) for milli- ([latex]0.001[/latex] times)
You can view the transcript for “Metric Conversion Trick!! Part 1” here (opens in new window).
Conversions between U.S. and Metric Measurement Systems
To convert between metric units and US standard units, you need to understand the relationship between the two systems of measurement and use conversion factors.
- Identify the starting unit and the unit you want to convert to.
- Look up the appropriate conversion factor for the units you are converting.
- Multiply the value you want to convert by the conversion factor.
- Round the result to the appropriate number of significant digits.
You can view the transcript for “How to convert metric to US Standard length/Centimeters,Kilometers,Inches” here (opens in new window).
Converting Between Temperatures
It might be helpful to understand how the temperature conversion formulas were created. They came from comparing the two scales. Since the freezing point is [latex]0°[/latex] in the Celsius scale and [latex]32°[/latex] on the Fahrenheit scale, we subtract [latex]32[/latex] when converting from Fahrenheit to Celsius, and add [latex]32[/latex] when converting from Celsius to Fahrenheit.
There is a reason for the fractions [latex]\frac{5}{9}[/latex] and [latex]\frac{9}{5}[/latex], also. There are [latex]100[/latex] degrees between the freezing ([latex]0°[/latex]) and boiling points ([latex]100°[/latex]) of water on the Celsius scale and [latex]180[/latex] degrees between the similar points ([latex]32°[/latex] and [latex]212°[/latex]) on the Fahrenheit scale. Writing these two scales as a ratio, [latex]\frac{F{}^\circ }{C{}^\circ }[/latex], gives [latex]\frac{180{}^\circ }{100{}^\circ }=\frac{180{}^\circ \div 20}{100{}^\circ \div 20}=\frac{9}{5}[/latex]. If you flip the ratio to be [latex]\frac{\text{C}{}^\circ }{\text{F}{}^\circ }[/latex], you get [latex]\frac{100{}^\circ }{180{}^\circ }=\frac{100{}^\circ \div 20}{180{}^\circ \div 20}=\frac{5}{9}[/latex]. Notice how these fractions are used in the conversion formulas.
The example below illustrates the conversion of Celsius temperature to Fahrenheit temperature, using the boiling point of water, which is [latex]100°[/latex] C.
You can view the transcript for “Temperature Conversion Trick (Celsius to Fahrenheit) | Infinity Learn NEET” here (opens in new window).