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Chapter 1: Basics
Metric System
Prefixes, powers of 10, and scientific notation
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Metric Prefixes
The metric system uses prefixes to express very large or very small numbers. Each step is a power of 10.
Prefix
Symbol
Power
Meaning
Giga
G
10⁹
Billion
Mega
M
10⁶
Million
Kilo
k
10³
Thousand
Hecto
h
10²
Hundred
Deca
da
10¹
Ten
Base unit
-
10⁰
One
Deci
d
10⁻¹
Tenth
Centi
c
10⁻²
Hundredth
Milli
m
10⁻³
Thousandth
Micro
μ
10⁻⁶
Millionth
Nano
n
10⁻⁹
Billionth
Think of the prefixes as a staircase. Each step up multiplies by 10. Each step down divides by 10.
Conversion Trick
Moving the decimal to the right makes the number bigger (going down in power). Moving the decimal to the left makes the number smaller (going up in power).
Scientific Notation
A shorthand for very large or small numbers. Write a number between 1 and 10, then multiply by a power of 10.
1234 = 1.234 × 10³
The decimal moved 3 places left, so the exponent is positive 3.
0.01234 = 1.234 × 10⁻²
The decimal moved 2 places right, so the exponent is negative 2.
Quick Rule
Positive exponent = big number (decimal moved left). Negative exponent = small number (decimal moved right).
SPI EXAM TOPIC
Prefixes You Will Use Constantly
Mega (M) for frequency: ultrasound operates in MHz (megahertz = millions of Hz). Milli (m) for wavelength: measured in mm (millimeters). Kilo (k) for speed: sound travels at about 1.54 km/s in soft tissue. Micro (μ) for time: pulse durations measured in μs (microseconds).
Why This Matters
Ultrasound physics involves numbers ranging from billionths to millions. Without metric prefixes and scientific notation, these would be impossible to work with. You will see these prefixes in every chapter going forward.