Scientific Units & Scientific Notation
Learn the standard units science uses, what metric prefixes mean, and how to write very large and very small biology numbers cleanly with powers of ten.
Biology numbers are extreme. One drop of blood holds millions of cells, the human genome is about three billion base pairs, and a drug can act at a concentration of a few millionths of a gram per liter. Writing all those zeros by hand is slow and easy to get wrong, so scientists agree on two things: a shared set of units (the SI system) and a compact way to write numbers (scientific notation). Lab technicians label every tube in milliliters and micrograms so no one confuses a safe dose with a lethal one. Geneticists report a genome as 3 x 10 to the 9th power base pairs instead of counting nine zeros. Pharmacists read a concentration in mg per mL and must know that milli means one thousandth before they draw up a syringe. Epidemiologists compare case counts written in scientific notation so a city of millions lines up cleanly next to a town of thousands. Master units and scientific notation and you can read, record, and check biology data without drowning in zeros.
- Common Core · HSN-Q.A.1Use units as a way to understand problems; choose and interpret the units and the level of accuracy that fit a measurement.
- Common Core · HSN-RN.AWork fluently with powers and exponents, including expressing and comparing numbers written with powers of ten.
- Ohio · Ohio HS N.Q.1Reason quantitatively and use units consistently when recording, reporting, and interpreting scientific measurements.
- NGSS · SEP-5Using Mathematics and Computational Thinking: use appropriate units and scientific notation to record and compare quantities across many orders of magnitude.
- AP · AP Bio SP 6 (Quantitative)Work with quantities and units, including very large and very small values, when analyzing and communicating biological data.
- Read and move a decimal point by place value: Scientific notation is all about counting how many places the decimal moves, so students must track place value confidently.
- Understand powers of ten (10^3 = 1000, 10^-3 = 1/1000): Prefixes and scientific notation both use positive and negative powers of ten, so students must know what an exponent means.
- Read a measurement as a number plus a unit: You cannot pick a prefix or a unit for a number you cannot name, so students must separate the number from its label first.
Prerequisites are inferred: pending teacher review.
Re-learn the skill with worked practice and clear examples.
Use the metric prefix ladder to move between sized units, and use scientific notation to write very large and very small numbers cleanly. To convert to scientific notation, put one nonzero digit in front of the decimal, then count how many places you moved it: moving left gives a positive exponent, moving right gives a negative exponent.
Using the prefix ladder, how many milligrams (mg) are in 1 gram (g)? Use the fact that milli means 10^-3.
Reviewed- A.10 mg
- B.100 mg
- C.1000 mg
- D.10,000 mg
Show the worked solution ▾
Answer: C. 1000 mg
- Step 1: Find the gap on the ladder: The gram is at 10^0 and the milligram is at 10^-3, so a milligram is 1000 times smaller than a gram.
- Step 2: Count the small units: If each milligram is one thousandth of a gram, it takes 1000 of them to make one whole gram.
Why it's right: The milligram sits three steps below the gram (10^-3), so 1 g = 1000 mg.
- A: 10 is only one step down (deci), not three steps to milli.
- B: 100 is only two steps down (centi), not three steps to milli.
- D: 10,000 is four steps of ten, which overshoots milli by one power of ten.
Aligned to Ohio HS N.Q.1: use metric prefixes · reading level ~grade 9
A blood sample is counted as 5,600,000 white blood cells. Write this number in scientific notation.
Reviewed- A.5.6 x 10^5
- B.5.6 x 10^6
- C.56 x 10^5
- D.5.6 x 10^-6
Show the worked solution ▾
Answer: B. 5.6 x 10^6
- Step 1: Place the decimal: Move the decimal so exactly one nonzero digit is in front: 5.6.
- Step 2: Count the places: The decimal moved 6 places to the left, and moving left makes the exponent positive, so the answer is 5.6 x 10^6.
Why it's right: Moving the decimal 6 places left turns 5,600,000 into 5.6 with a positive exponent of 6, so 5,600,000 = 5.6 x 10^6.
- A: This is only 560,000; the decimal was moved just 5 places.
- C: The front number must be between 1 and 10, and 56 is not.
- D: A negative exponent would mean a tiny number less than one, but 5,600,000 is large.
Aligned to Common Core HSN-RN.A: scientific notation for large numbers · reading level ~grade 9
A drug concentration is measured as 0.000018 grams per liter. Write 0.000018 in scientific notation.
Reviewed- A.1.8 x 10^-4
- B.1.8 x 10^-5
- C.1.8 x 10^5
- D.18 x 10^-6
Show the worked solution ▾
Answer: B. 1.8 x 10^-5
- Step 1: Place the decimal: Move the decimal so one nonzero digit is in front: 1.8.
- Step 2: Count the places: The decimal moved 5 places to the right, and moving right makes the exponent negative, so the answer is 1.8 x 10^-5.
Why it's right: Moving the decimal 5 places right turns 0.000018 into 1.8 with a negative exponent of 5, so 0.000018 = 1.8 x 10^-5.
- A: This is 0.00018; the decimal was moved only 4 places.
- C: A positive exponent would make the number large, but 0.000018 is tiny.
- D: The front number must be between 1 and 10, and 18 is not.
Aligned to Common Core HSN-RN.A: scientific notation for small numbers · reading level ~grade 9
- A lab tech writes a bacterial count of 8,300,000 colonies as 8.3 x 10^6 so it fits neatly in the data table.
- A student converts a stock solution of 0.25 L into 250 mL to match the graduated cylinder markings.
- A researcher records a protein concentration of 0.000045 g/mL as 4.5 x 10^-5 g/mL for the report.
Fill these in as you work through the lesson.
- SI base unit (the standard unit for a quantity, like meter, kilogram, second):
- Metric prefix (a word piece that multiplies a unit by a power of ten):
- Scientific notation (a value between 1 and 10 times a power of ten):
- Exponent (the power of ten; positive is big, negative is small):
To write a number in scientific notation, put one nonzero digit in front of the decimal and count the places you moved it: moving gives a positive exponent, and moving gives a exponent.
- Name the five SI base units in this lesson and the quantity each one measures.
- On the prefix ladder, how many powers of ten separate milli from micro, and which one is smaller?
- Explain how the sign of the exponent tells you whether a number is large or small.
Write 3,200,000 in scientific notation. Put one nonzero digit in front of the decimal to get 3.2, then count the places you moved the decimal to the left, which is 6, so 3,200,000 = 3.2 x 10^____.
The vocabulary of this topic, shown in the way you will meet it.
| Quantity | SI base unit | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | kilogram | kg |
| Time | second | s |
| Amount of substance | mole | mol |
| Temperature | kelvin | K |