How to read and convert scientific notation and metric prefixes, the two skills the HESI A2 Chemistry subtest leans on before it ever asks a reaction question.
ObjectiveC.1.1Read5 minExam weightMatter and Measurement ≈ 28% of Chemistry
By the end of this lesson you can
Convert a number between standard form and scientific notation in either direction.
Move a metric measurement between prefixes (kilo, centi, milli, micro) without a calculator.
Read a lab or medication value written in scientific notation or metric units and know what it means for a patient.
Key takeaways
Scientific notation writes a number as a digit between one and ten, times ten raised to a power.
A positive exponent means a large number; a negative exponent means a small number.
The metric system is built entirely on multiples of ten, so converting between prefixes is a matter of moving the decimal point.
Kilo, centi, and milli are the three prefixes you will meet most often on medication labels and lab reports.
Getting a decimal point one place wrong in either system changes a dose or a lab value by a factor of ten.
Check yourself
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1In scientific notation, a number is written as a leading digit multiplied by ten raised to a power. What range must that leading digit fall into?
2A value in scientific notation has a negative exponent. What does that tell you about the size of the number?
3A particle count of 27,000 needs to be written in scientific notation. Which of the following is correct?
4A colleague converts 0.0038 into scientific notation and writes 3.8 × 10³. What is actually wrong with this answer?
5You are simplifying (4 × 10²) × (2 × 10⁵) and have already multiplied the leading numbers, 4 and 2, to get 8. What is the correct next step?
Scientific notation and the metric system run underneath much of HESI A2 Chemistry, not because the exam tests them directly very often, but because you need both fluently to get through density, concentration, and stoichiometry questions without losing time to arithmetic. Get comfortable here first.
Scientific notation, in plain terms
Scientific notation writes any number as a single digit from one to nine, optionally followed by a decimal point and more digits, multiplied by ten raised to a power. The general form is:
a × 10ⁿ, where a is at least 1 and less than 10, and n is an integer (positive, negative, or zero).
The exponent tells you which direction, and how far, to move the decimal point.
Standard number
Scientific notation
What the exponent means
5,400,000
5.4 × 10⁶
move the decimal six places right to get back to standard form
320
3.2 × 10²
move the decimal two places right
0.00072
7.2 × 10⁻⁴
move the decimal four places left
0.0009
9 × 10⁻⁴
move the decimal four places left
To convert standard form to scientific notation, count how many places you move the decimal until only one non-zero digit remains to its left. Moving the decimal left gives a positive exponent (the original number was large); moving it right gives a negative exponent (the original number was small, a fraction).
Multiplying and dividing in scientific notation. Multiply the leading numbers and add the exponents; divide the leading numbers and subtract the exponents. So (2 × 10³) × (3 × 10²) = 6 × 10⁵, and (6 × 10⁶) ÷ (2 × 10²) = 3 × 10⁴.
The metric system: one scale, built on ten
The metric system measures length, volume, mass, and other quantities on a single logical scale, where every step between units is a power of ten. That single design choice is why nursing and laboratory work runs on metric units almost everywhere in the world: there is no need to remember odd conversion factors like twelve inches to a foot or sixteen ounces to a pound.
Every metric measurement has two parts: a base unit (metre for length, litre for volume, gram for mass) and a prefix that scales that base unit up or down by a power of ten.
Prefix
Symbol
Multiplier relative to the base unit
kilo
k
1,000 times the base unit
(base unit)
m, L, g
1
deci
d
0.1 of the base unit
centi
c
0.01 of the base unit
milli
m
0.001 of the base unit
micro
µ (mc in clinical use)
0.000001 of the base unit
Because each step is a multiple of ten, converting between prefixes is the same skill as converting between standard form and scientific notation: you are only moving a decimal point.
Why this matters at the bedside. A decimal point placed one position wrong turns 0.5 mg into 5 mg, a tenfold overdose. The HESI tests the arithmetic, but the arithmetic exists because real medication safety depends on it.
Reading the two together
Lab systems and drug references often report very large or very small metric quantities in scientific notation rather than writing out long strings of zeros. A haemoglobin A1c assay might store its raw absorbance reading as 3.4 × 10⁻² in a units field before the software converts it to a percentage, and a blood cell count is routinely reported as cells × 10⁹/L. Recognising both notations together, and converting confidently between them, is what lets you move quickly through a HESI Chemistry question that stacks a metric conversion and a scientific notation step in the same problem, rather than getting stuck counting zeros by hand.
The exponent tells you how far to move the decimal, and the prefix tells you which unit you are moving it in.
Practise both conversions until moving a decimal point feels automatic, then move on to significant figures, where the same careful reading of a number pays off again.