Formulas, Units & Conversion Reference Tables - Fourth Grade Science
In physical and biological science, precision is everything. A scientist cannot simply report that an object is "heavy," that a car moved "fast," or that a liquid felt "warm." To understand natural systems, test hypotheses, and verify experimental results, scientists rely on standardized units of measurement, mathematical formulas, and reliable conversion tables. The global scientific community utilizes the International System of Units (SI), commonly known as the metric system, ensuring that researchers worldwide speak the identical quantitative language. This chapter serves as your master mathematical reference toolkit for fourth grade science, containing the fundamental formulas, measurement units, and conversion factors you will use throughout your investigations.
The International System of Units (SI Metric Base Units)
The metric system is a base-ten decimal system organized around standard fundamental units of measurement. Every unit expands or contracts by factors of ten using standardized prefixes.
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| SI METRIC BASE AND DERIVED UNITS |
| |
| Physical Quantity | Unit Name | Standard Symbol |
| ------------------- | -------------------- | ------------------ |
| Length / Distance | Meter | m |
| Mass | Gram / Kilogram | g / kg |
| Liquid Volume | Liter / Milliliter | L / mL |
| Time | Second | s |
| Temperature | Degrees Celsius | deg C |
| Force / Weight | Newton | N |
| Energy / Work | Joule | J |
| Frequency | Hertz | Hz |
| Electrical Current | Ampere | A |
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The Metric Prefix Ladder
Metric units utilize prefixes that indicate multiplication or division by powers of ten. Remembering these prefixes makes metric calculations simple:
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| THE METRIC PREFIX LADDER |
| |
| Kilo- (k) = 1,000 times base unit (1 km = 1,000 m) |
| Hecto- (h) = 100 times base unit (1 hm = 100 m) |
| Deka- (da) = 10 times base unit (1 dam = 10 m) |
| [ BASE UNIT: Meter, Gram, Liter, Second ] = 1 |
| Deci- (d) = 1/10 of base unit (0.1) (1 dm = 0.1 m) |
| Centi- (c) = 1/100 of base unit (0.01)(1 cm = 0.01 m) |
| Milli- (m) = 1/1,000 of base unit (1 mm = 0.001 m) |
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Essential Science Formulas
Throughout fourth grade science, you will apply several core mathematical formulas to calculate speed, work, density, and wave behavior:
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| MASTER SCIENTIFIC FORMULAS |
| |
| Quantity to Find | Mathematical Formula | Measurement Units |
| ------------------- | -------------------- | ------------------ |
| Speed | Speed = Distance / T | m/s or km/h |
| Mechanical Work | Work = Force x Dista | Joules (J) = N x m |
| Density | Density = Mass / Vol | g/cm^3 or g/mL |
| Mechanical Advantag | MA = Output / Input | Pure Ratio (No unit|
| Wave Speed | Speed = Wavelen x Fr | m/s = m x Hz |
| Net Force | F_net = F_1 + F_2... | Newtons (N) |
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Speed Formula
Speed measures how fast an object travels across a given distance:
$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$
If a toy battery-powered car travels a distance of 12 meters across a classroom floor in 4 seconds, its speed is 3 meters per second ($12\text{ m} / 4\text{ s} = 3\text{ m/s}$).
Mechanical Work Formula
Work occurs when an applied force causes an object to move across a distance:
$$\text{Work} = \text{Force} \times \text{Distance}$$
Work is measured in Joules (J). One Joule equals one Newton of force applied across a distance of one meter ($1\text{ J} = 1\text{ N} \times 1\text{ m}$). If you lift a backpack weighing 20 Newtons vertically onto a table 1.5 meters high, you perform 30 Joules of mechanical work ($20\text{ N} \times 1.5\text{ m} = 30\text{ J}$).
Density Formula
Density measures how tightly packed the mass of an object is within a given volume:
$$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$$
Pure liquid water has a density of exactly 1.0 grams per cubic centimeter ($1.0\text{ g/cm}^3$, or $1.0\text{ g/mL}$). Any solid object with a density greater than $1.0\text{ g/cm}^3$ (like an iron nail) will sink in water; any object with a density less than $1.0\text{ g/cm}^3$ (like a pine block or wax candle) will float.
Metric and Standard Unit Conversion Tables
In everyday American life, customary units (inches, pounds, gallons) are common, but scientific laboratories operate strictly in metric units. The following reference tables provide common conversion values:
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| LENGTH CONVERSION TABLE |
| |
| Customary Unit | Metric Equivalent |
| --------------------- | --------------------------------------- |
| 1 inch (in) | exactly 2.54 centimeters (cm) |
| 1 foot (ft = 12 in) | 30.48 centimeters (0.3048 meters) |
| 1 yard (yd = 3 ft) | 0.914 meters (91.4 cm) |
| 1 mile (mi = 5,280 ft)| 1.609 kilometers (1,609 meters) |
| 1 meter (m) | 39.37 inches (3.28 feet) |
| 1 kilometer (km) | 0.621 miles |
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| MASS AND WEIGHT CONVERSION TABLE |
| |
| Customary Unit | Metric Equivalent |
| --------------------- | --------------------------------------- |
| 1 ounce (oz) | 28.35 grams (g) |
| 1 pound (lb = 16 oz) | 453.6 grams (0.4536 kilograms) |
| 1 kilogram (kg) | 2.205 pounds (on Earth's surface) |
| 1 metric ton (1,000 kg| 2,204.6 pounds |
| 1 Newton (N of force) | 0.225 pounds of force (about 1 apple) |
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| VOLUME CONVERSION TABLE |
| |
| Customary Unit | Metric Equivalent |
| --------------------- | --------------------------------------- |
| 1 fluid ounce (fl oz) | 29.57 milliliters (mL) |
| 1 cup (8 fl oz) | 236.6 milliliters (mL) |
| 1 pint (2 cups) | 473.2 milliliters (mL) |
| 1 quart (2 pints) | 946.4 milliliters (0.946 liters) |
| 1 gallon (4 quarts) | 3.785 liters (L) |
| 1 liter (L) | 1.057 quarts (1,000 milliliters) |
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Temperature Comparison Scales: Celsius versus Fahrenheit
Scientists measure temperature in degrees Celsius (deg C), while everyday household thermometers in the United States often display degrees Fahrenheit (deg F).
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| TEMPERATURE BENCHMARK POINTS |
| |
| Benchmark Event | Celsius (deg C) | Fahr (deg F)|
| --------------------------- | --------------- | ----------- |
| Absolute Zero (No motion) | -273.15 deg C | -459.67 deg |
| Freezing Point of Water | 0 deg C | 32 deg F |
| Average Room Temperature | 20 to 22 deg C | 68 to 72 deg|
| Normal Human Body Temp | 37 deg C | 98.6 deg F |
| Boiling Point of Water | 100 deg C | 212 deg F |
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Temperature Conversion Formulas
To convert between Celsius and Fahrenheit mathematically, use these equations:
From Celsius to Fahrenheit: $$^{\circ}\text{F} = (^{\circ}\text{C} \times 1.8) + 32$$
From Fahrenheit to Celsius: $$^{\circ}\text{C} = \frac{^{\circ}\text{F} - 32}{1.8}$$
Chapter Practice Exercises
Question 1: If a student walks a distance of 400 meters in 200 seconds, what is the student's average speed in meters per second?
Question 2: An engine uses a force of 500 Newtons to pull a cart across a distance of 10 meters. How many Joules of mechanical work were performed?
Question 3: A rock sample has a mass of 45 grams and displaces a volume of 15 milliliters of water in a graduated cylinder. Calculate the density of the rock sample and state whether it will sink or float in pure water.
Question 4: Convert a temperature of 25 degrees Celsius (a warm spring day) into degrees Fahrenheit using the standard conversion formula.
Solutions and Explanations
Solution 1: Using the speed formula ($\text{Speed} = \text{Distance} / \text{Time}$), divide 400 meters by 200 seconds ($400\text{ m} / 200\text{ s} = 2\text{ m/s}$). The student's average walking speed is 2 meters per second.
Solution 2: Using the mechanical work formula ($\text{Work} = \text{Force} \times \text{Distance}$), multiply 500 Newtons by 10 meters ($500\text{ N} \times 10\text{ m} = 5,000\text{ J}$). The engine performs 5,000 Joules of work.
Solution 3: Using the density formula ($\text{Density} = \text{Mass} / \text{Volume}$), divide 45 grams by 15 milliliters ($45\text{ g} / 15\text{ mL} = 3.0\text{ g/mL}$). The density of the rock is $3.0\text{ g/mL}$. Because its density is greater than the density of pure water ($1.0\text{ g/mL}$), the rock will sink to the bottom.
Solution 4: Using the formula $^{\circ}\text{F} = (^{\circ}\text{C} \times 1.8) + 32$: first multiply 25 by 1.8, which equals 45. Then add 32 ($45 + 32 = 77$). Therefore, 25 degrees Celsius is exactly equal to 77 degrees Fahrenheit.