Metric System Measurements

Metric System

• The metric system uses the following prefixes: Kilo, Hecto, Deka, UNIT, Deci, Centi, Milli.
• The metric system is used to measure: meters (length), liters (volume), grams (mass).

Length

• 1 inch (in) = 2.54 centimeters (cm)
• 1 foot (ft) = 30.48 cm = 0.3048 meters (m)
• 1 yard (yd) = 91.44 cm = 0.9144 m
• 1 mile (mi) ≈ 1.61 kilometers (km)
• 1 millimeter (mm) ≈ 0.03937 in
• 1 centimeter (cm) ≈ 0.3937 in
• 1 meter (m) ≈ 1.0936 yd = 3.2808 ft
• 1 kilometer (km) ≈ 0.6214 mi
• 1 foot (ft) = 12 inches (in)
• 1 yard (yd) = 3 ft
• 1 yard (yd) = 36 in
• 1 mile (mi) = 5280 ft
• 1 mile (mi) = 1760 yd

Area

• 1 square foot (ft2) = 144 square inches (in2)
• 1 square yard (yd2) = 9 ft2 = 1296 in2
• 1 square mile (mi2) = 27,878,400 ft2 = 3,097,600 yd2
• 1 acre = 43,560 ft2
• 1 square mile (mi2) = 640 acres
• 1 square inch (in2) ≈ 6.45 cm2
• 1 square foot (ft2) ≈ 0.093 m2
• 1 square yard (yd2) ≈ 0.836 m2
• 1 square mile (mi2) ≈ 2.59 km2
• 1 acre ≈ 4,047 m2

Volume

• 1 pint (pt) = 16 ounces (oz)
• 1 quart (qt) = 2 pt
• 1 gallon (gal) = 4 qt
• 1 pint (pt) = 2 cups
• 1 cup = 8 oz
• 1 gallon (gal) = 128 oz
• 1 cubic foot (ft3) ≈ 7.48 gal
• 1 cubic yard (yd3) ≈ 201.97 gal
• 1 gallon (gal) ≈ 231 in3
• 1 cubic foot (ft3) of fresh water ≈ 62.5 lb
• 1 cubic foot (ft3) of salt water ≈ 64 lb
• 1 cubic centimeter (cm3) = 1 milliliter (mL) = 1 gram (g) = 1000 mm3
• 1 cubic decimeter (dm3) = 1000 cm3 = 1 liter (L) = 1 kilogram (kg)
• 1 cubic meter (m3) = 1000 dm3 = 1 kiloliter (kL) = 1,000 L
• 1 liter (L) ≈ 1.06 qt
• 1 gallon (gal) ≈ 3.7854 L
• 1 quart (qt) ≈ 0.9464 L
• 1 ounce (oz) ≈ 29.5735 mL
• 1 cubic foot (ft3) = 1728 in3
• 1 cubic yard (yd3) = 27 ft3
• 1 cubic foot (ft3) ≈ 0.02832 m3
• 1 cubic yard (yd3) ≈ 0.7646 m3

Weight

• 1 pound (lb) = 16 ounces (oz)
• 1 ton (T) = 2,000 lb
• 1 ton (T) ≈ 0.9072 metric ton (t)
• 1 kilogram (kg) = 1000 grams (g)
• 1 metric ton (t) = 1,000 kg
• 1 kilogram (kg) ≈ 2.2 lb
• 1 ounce (oz) ≈ 28 g

Time

• 1 minute (min) = 60 seconds (sec)
• 1 hour = 60 min
• 1 day = 24 hours
• 1 year = 365 days

Percentage

• To find a percentage, divide the part by the whole and multiply by 100.
• Percentage = Rate * Base

Math Formulas

• Slope-Intercept Form: 𝑦 = 𝑚𝑥 + 𝑏 , where 𝑚 is the slope and 𝑏 is the y-intercept.
• Slope Formula: 𝑚 = (𝑦2 − 𝑦1) / (𝑥2 − 𝑥1)
• Celsius to Fahrenheit Conversion:  𝐹= (9/5)𝐶 + 32
• Fahrenheit to Celsius Conversion: 𝐶 = (5/9)(𝐹 − 32)
• Simple Interest: 𝐼 = 𝑃𝑟𝑡 , where 𝐼 is interest, 𝑃 is principle, 𝑟 is rate and 𝑡 is time
• Compound Interest: 𝐴 = 𝑃(1 + 𝑟/𝑛) 𝑛𝑡 , where 𝐴 is the final amount, 𝑃 is the principle, 𝑟 is the rate, 𝑡 is the time, and 𝑛 is the number of times compounded per year.
• Future Value: 𝐴 = 𝑃 + 𝐼
• Present Value: 𝑃 = 𝐴 / (1 + 𝑟/𝑛) 𝑛𝑡
• Range: highest value – lowest value
• Pythagorean Theorem: 𝑎2 + 𝑏 2 = 𝑐 2

Geometry Formulas

• Area of a Rectangle: 𝐴 = 𝐿𝑤, where 𝐿 is length and 𝑤 is width.
• Perimeter of a Rectangle: 𝑃 = 2(𝐿) + 2(𝑤)
• Area of a Square: 𝐴 = 𝑠2, where 𝑠 is the side length.
• Perimeter of a Square: 𝑃 = 4𝑠
• Area of a Parallelogram: 𝐴= 𝑏ℎ, where 𝑏 is the base and ℎ is the height.
• Perimeter of a Parallelogram: 𝑃 = 2(𝑏) + 2(ℎ)
• Area of a Triangle: 𝐴 = (1/2) 𝑏ℎ, where 𝑏 is the base and ℎ is the height.
• Perimeter of a Triangle: 𝑃 = 𝑠1 + 𝑠2 + 𝑠3, where 𝑠 represents the side lengths.
• Area of a Trapezoid: 𝐴 = (1/2) ℎ(𝑎 + 𝑏), where 𝑎 and 𝑏 are the parallel sides and ℎ is the height.
• Perimeter of a Trapezoid: 𝑃 = 𝑠1 + 𝑠2 + 𝑠3 + 𝑠4, where 𝑠 represents the side lengths.
• Area of a Circle: 𝐴 = 𝜋𝑟 2, where 𝜋 is the constant (approximately 3.14) and 𝑟 is the radius.
• Circumference of a Circle: 𝐶 = 𝜋𝑑, where 𝜋 is the constant (approximately 3.14) and 𝑑 is the diameter.
• Circumference of a Circle: 𝐶 = 2𝜋𝑟, where 𝜋 is the constant (approximately 3.14) and 𝑟 is the radius.
• Volume of a Cube: 𝑉 = 𝑠3, where 𝑠 is the side length.
• Surface Area of a Cube: 𝑆𝐴 = 6𝑠 2, where 𝑠 is the side length.
• Volume of a Sphere: 𝑉 = (4/3)𝜋𝑟 3, where 𝜋 is the constant (approximately 3.14) and 𝑟 is the radius.
• Surface Area of a Sphere: 𝑆𝐴 = 4𝜋𝑟 2, where 𝜋 is the constant (approximately 3.14) and 𝑟 is the radius.
• Volume of a Rectangular Prism: 𝑉 = 𝐿𝑤ℎ, where 𝐿 is the length, 𝑤 is the width, and ℎ is the height.
• Surface Area of a Rectangular Prism: 𝑆𝐴 = 2𝐿𝑤 + 2𝑤ℎ + 2𝐿ℎ, where 𝐿 is the length, 𝑤 is the width, and ℎ is the height.
• Volume of a Cylinder: 𝑉 = 𝜋𝑟 2 ℎ, where 𝜋 is the constant (approximately 3.14), 𝑟 is the radius, and ℎ is the height.
• Surface Area of a Cylinder: 𝑆𝐴 = 2𝜋𝑟ℎ + 2𝜋𝑟 2, where 𝜋 is the constant (approximately 3.14), 𝑟 is the radius, and ℎ is the height.
• Volume of a Cone: 𝑉 = (1/3)𝜋𝑟 2 ℎ, where 𝜋 is the constant (approximately 3.14), 𝑟 is the radius, and ℎ is the height.
• Surface Area of a Cone: 𝑆𝐴 = 𝜋𝑟 + 𝜋𝑟√𝑟 2 + ℎ 2 , where 𝜋 is the constant (approximately 3.14), 𝑟 is the radius, and ℎ is the height.
• Sum of Interior Angles of a Polygon: (𝑛 − 2) ∙ 180°, where 𝑛 is the number of sides.

Properties of Exponents

• 𝑎𝑚 ∙ 𝑎𝑛 = 𝑎𝑚+𝑛
• 𝑎𝑚 / 𝑎𝑛 = 𝑎𝑚−𝑛 , 𝑎 ≠ 0
• (𝑎𝑚) 𝑛 = 𝑎𝑚∙𝑛
• 𝑎−𝑛 = 1 / 𝑎𝑛 , 𝑎 ≠ 0
• 𝑎0 = 1 , 𝑎 ≠ 0