How to measure like a scientist: units, prefixes, tools and readings
TEAS 7 outline: Use basic scientific measurements and measuring tools
Also covers HESI A2 Chemistry (Measurement and scientific notation)
- Science uses metric (SI) units: meters, grams, liters, seconds and kelvins.
- Prefixes change a unit by powers of ten: kilo, centi, milli, micro.
- Read a graduated cylinder at the bottom of the meniscus, at eye level.
- K = °C + 273.15; one Celsius degree equals one kelvin.
- Accurate means close to the true value; precise means repeatable.
Key facts
- SI base units include the meter (length), kilogram (mass), second (time), kelvin (temperature) and mole (amount of substance).
- Prefixes: kilo = 1,000; centi = 1/100; milli = 1/1,000; micro (µ) = 1/1,000,000 of the base unit.
- 1 liter = 1,000 mL, and 1 mL equals 1 cubic centimeter (cm³).
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- Read a graduated cylinder at the bottom of the meniscus with your eye level with it, recording all certain digits plus one estimated digit (to 0.1 mL on a cylinder marked every 1 mL).
- Water freezes at 0 °C, 32 °F and 273.15 K, and boils at 100 °C, 212 °F and 373.15 K; K = °C + 273.15 and °F = (9/5 × °C) + 32.
- A change of 1 Celsius degree equals a change of 1 kelvin; a Fahrenheit degree is smaller. 0 K is absolute zero, the lowest temperature possible.
- Accuracy is closeness to the true value; precision is closeness of repeated measurements to each other.
Quick check1 question · 2 more at the end
A water bath is heated from 25 °C to 60 °C. By how much did its temperature increase on the kelvin scale?
Correct answer: C.
A kelvin and a Celsius degree are the same size, so a temperature change in kelvins equals the change in degrees Celsius. The bath warmed by 60 − 25 = 35 °C, which is also 35 K. Add 273.15 only when converting a single temperature reading, not a difference between two readings.
A 63 K multiplies the 35-degree change by 9/5, which converts Celsius degrees to Fahrenheit degrees, not to kelvins.
B 308 K adds 273 to the 35-degree change, treating a temperature difference as if it were a single temperature reading.
C Correct: a 35 °C change is a 35 K change because the two units are the same size.
D 333 K is the final temperature of the bath in kelvins (60 + 273), not how much it increased.
Full lesson
Each part starts with its main idea. Open a part when you want the details.
The short answer: Science uses metric (SI) units: meters for length, grams and kilograms for mass, liters for volume, seconds for time and kelvins for temperature. Prefixes like kilo, centi, milli and micro change a unit by powers of ten. Read a graduated cylinder at the bottom of the meniscus. Accurate means close to the true value; precise means repeatable.
1 Which units does science use?Scientists around the world use the International System of Units (SI), the modern metric system. 1 min
Scientists around the world use the International System of Units (SI), the modern metric system. A few base units cover most of what you will measure:
| Quantity | SI unit (symbol) | Common lab tool |
|---|---|---|
| Length | meter (m) | Metric ruler or meter stick |
| Mass | kilogram (kg); grams (g) in the lab | Balance |
| Volume | liter (L) and milliliter (mL) | Graduated cylinder |
| Temperature | kelvin (K); degrees Celsius (°C) in the lab | Thermometer |
Time is measured in seconds (s), and the mole (mol) counts amount of substance. The liter is not itself an SI unit but is accepted for use with SI; it is the everyday name for a cubic decimeter. One milliliter equals one cubic centimeter (cm³), so 1 L = 1,000 mL = 1,000 cm³.
Mass vs. weight: Mass is the amount of matter in an object, and it stays the same anywhere, even on the moon. Weight is the force gravity exerts on that object, so it changes when gravity changes. A lab balance reports mass in grams.
2 How do metric prefixes work?A prefix makes a unit larger or smaller by a power of ten. 1 min
A prefix makes a unit larger or smaller by a power of ten. The prefix is the same whether the unit is meters, grams or liters.
| Prefix (symbol) | Meaning | Example |
|---|---|---|
| kilo (k) | 1,000 × | 1 km = 1,000 m |
| (base unit) | 1 | 1 g |
| deci (d) | 1/10 | 1 dL = 0.1 L |
| centi (c) | 1/100 | 1 cm = 0.01 m |
| milli (m) | 1/1,000 | 1 mg = 0.001 g |
| micro (µ) | 1/1,000,000 | 1 µg = 0.000001 g |
To convert, decide whether the new unit is smaller or larger. Going to a smaller unit gives a bigger number: 2.5 L = 2,500 mL. Going to a larger unit gives a smaller number: 750 mg = 0.75 g. For metric-to-US conversions you will be given a factor, such as 1 inch = 2.54 cm.
3 How do you read a graduated cylinder?Water in a narrow glass cylinder curves into a shape called the meniscus. 1 min
Water in a narrow glass cylinder curves into a shape called the meniscus. Always read the volume at the bottom of the meniscus, its lowest point. Bend down so your eye is level with it. Looking from above or below makes the liquid seem to line up with a different mark. This error is called parallax.
Then record every digit you are sure of plus one estimated digit. On a cylinder marked every 1 mL, imagine the space between two marks split into tenths and estimate to the nearest 0.1 mL. Say the bottom of the curve sits about seven-tenths of the way from 52 to 53 mL. You record 52.7 mL: the 5 and 2 are certain, and the 7 is your best guess.
The same idea applies to every instrument. An electronic balance showing 3.48 g means the mass is likely between 3.47 and 3.49 g. Writing more digits than the tool can support claims precision you do not have.
4 How do Celsius, Fahrenheit and kelvin compare?Celsius divides the range from freezing to boiling into 100 degrees, while Fahrenheit divides it into 180, so a Fahrenheit degree is smaller. 1 min
| Reference point | Celsius | Fahrenheit | Kelvin |
|---|---|---|---|
| Water freezes | 0 °C | 32 °F | 273.15 K |
| Normal body temperature | 37.0 °C | 98.6 °F | 310.2 K |
| Water boils | 100 °C | 212 °F | 373.15 K |
The conversions:
- K = °C + 273.15
- °F = (9/5 × °C) + 32
- °C = 5/9 × (°F − 32)
Celsius divides the range from freezing to boiling into 100 degrees, while Fahrenheit divides it into 180, so a Fahrenheit degree is smaller. A Celsius degree and a kelvin are the same size: warming something by 10 °C warms it by 10 K.
Kelvin values are written without a degree sign: 310 K, not 310 °K. The kelvin scale starts at absolute zero (0 K), the coldest temperature possible in theory, so kelvin temperatures are never negative.
5 What is the difference between accurate and precise?Accuracy is how close a measurement is to the true or accepted value. 1 min
Accuracy is how close a measurement is to the true or accepted value. Precision is how close repeated measurements are to each other.
Picture arrows on a target. Arrows clustered in the bull's-eye are accurate and precise. Arrows clustered tightly off to one side are precise but not accurate, which is what a balance that is off by a fixed amount produces. Arrows scattered everywhere are neither. Repeating a measurement shows precision; comparing it to a known standard shows accuracy.
Common mistakes
The traps students fall into most. Read these before you practice.
Watch out: Read the bottom of the meniscus, not the top edge where the liquid climbs the glass.
Watch out: Mass is the amount of matter and does not change on the moon; weight is the pull of gravity and does change.
Watch out: Precise does not mean accurate: results can agree closely with each other and still all be wrong.
Watch out: To change °C to kelvins you add 273.15; the 9/5 factor is only for Fahrenheit, and kelvins are written without a degree sign.
Watch out: A milligram is smaller than a centigram, and a microgram is smaller still; more letters do not mean bigger.
How to remember it
Memory hook: "King Henry Died By Drinking Chocolate Milk" lists kilo, hecto, deka, base, deci, centi, milli in order, each step ten times smaller. Micro sits three steps beyond milli.
Self-check:
- Put 1 mg, 1 kg, 1 µg and 1 g in order from smallest to largest.
- A cylinder is marked every 1 mL. To how many decimal places should you record its reading, and where on the liquid do you look?
- A sample warms from 20 °C to 45 °C. By how many kelvins did it warm?
Show answers
- 1 µg, 1 mg, 1 g, 1 kg. Step 1: write each one in grams. 1 µg = 0.000001 g, 1 mg = 0.001 g, 1 g = 1 g, 1 kg = 1,000 g. Step 2: order the numbers from smallest to largest.
- One decimal place (to the nearest 0.1 mL). Step 1: the marks are 1 mL apart, so the ones digit is certain. Step 2: add one estimated digit, the tenths. Step 3: look at the bottom of the meniscus, with your eye level with it.
- 25 K. Step 1: find the change in Celsius: 45 − 20 = 25 °C. Step 2: a Celsius degree and a kelvin are the same size, so the change is 25 K. Check: 20 + 273.15 = 293.15 K and 45 + 273.15 = 318.15 K; 318.15 − 293.15 = 25 K.