HESI A2 · Chemistry · 6 min read
Scientific Notation and Significant Figures
- Identify standard metric units and metric prefixes used in scientific measurements.
- Convert, multiply, divide, add, and subtract values using proper scientific notation.
- Apply significant figure rules to measurement readings, calculations, and rounding.
The Metric System and Scientific Units of Measurement
In scientific laboratories and healthcare environments, standard communication depends on clear, shared units. The International System of Units (SI) is the standard metric system used in scientific measurements. By relying on standardized units, practitioners communicate what quantity was measured, although measured values still have uncertainty.
Different types of physical quantities rely on specific standard units within the metric system. In the metric system, the standard base unit for length is the meter. In chemistry, mass is standardly measured using the gram or the kilogram, depending on the scale of the material being evaluated. For fluids, the liter is the standard metric unit used to measure liquid volume. In everyday clinical and laboratory tasks, liquid volumes and spatial volumes are frequently connected through a direct equality: one milliliter is exactly equivalent in volume to one cubic centimeter.
Metric measurements are organized in increments of ten, making conversions straightforward. For instance, one liter equals 1,000 milliliters. When measuring mass, one kilogram equals 1,000 grams, one gram equals 1,000 milligrams, and one milligram equals 1,000 micrograms. Exact conversion factors within the same measurement system possess an infinite number of significant figures, which means that using these established relationships during unit conversions will never restrict or reduce the precision of your calculated values.
To express smaller or larger increments of these base units, standardized prefixes are attached to the unit name. Each prefix represents a specific multiplier written as an ordinary number or as a power of 10. The table below details these metric prefixes and their corresponding numerical values.
| Metric Prefix | Multiplier (Standard Decimal) | Multiplier (Power of 10) |
|---|---|---|
| kilo- | 1,000 | 10 to the third power |
| hecto- | 100 | 10 to the second power |
| deka- | 10 | 10 to the first power |
| deci- | 0.1 | 10 to the negative first power |
| centi- | 0.01 | 10 to the negative second power |
| milli- | 0.001 | 10 to the negative third power |
| micro- | 0.000001 | 10 to the negative sixth power |
| nano- | 0.000000001 | 10 to the negative ninth power |
Common mistakes
- Treating leading zeros as significant figures; leading zeros appear before the first non-zero digit and function solely as placeholders to locate the decimal point (for example, 0.0025 contains only two significant figures).
- Applying the significant figure count rule to addition or subtraction; addition and subtraction must be rounded to the least precise decimal place among the measured values, not to the fewest total significant figures.
- Assuming whole numbers with trailing zeros have a definite precision; trailing zeros in a whole number without a written decimal point are ambiguous unless precision is specified (such as using scientific notation or placing a decimal point at the end, as in 500.).
- Rounding intermediate values during multi-step problems; rounding should only be performed on the final result in a multi-step calculation to avoid intermediate rounding error.
Key points
- SI uses the meter for length, the kilogram for mass, and the cubic meter for volume; grams and liters are also commonly used in metric measurements, and 1 milliliter equals exactly 1 cubic centimeter.
- Metric prefixes modify base units by powers of ten, ranging from kilo- (1,000 or 10 to the third power) down to nano- (0.000000001 or 10 to the negative ninth power).
- Scientific notation expresses a nonzero number as a coefficient whose absolute value is at least 1 and strictly less than 10, multiplied by 10 raised to an integer exponent.
- When working with scientific notation, multiply coefficients and add exponents, divide coefficients and subtract exponents, or equate exponents before adding or subtracting.
- In measured values, nonzero digits and captive zeros are significant, leading zeros are not, and trailing zeros are significant when indicated by a decimal point or otherwise specified by the measurement’s stated precision; analog readings generally include one estimated final digit.
- Exact numbers from counting individual objects and exact conversions within the same measurement system possess an infinite number of significant figures.
- Calculations must be rounded appropriately: match the fewest significant figures for multiplication and division, match the least precise decimal place for addition and subtraction, and round only the final result.
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