Question

test your knowledge 1
rank the si prefixes in order from smallest to largest.
smallest
2.0 x 10^-6 m
1.0 x10^-5 m
1.0 m
3.0 x 10^-7 m
4.0 x 10^3 mm
largest

Explanation:

Step1: Convert all units to meters

• \(2.0\times10^{-6}\text{ m}\) (already in meters)
• \(1.0\times10^{-5}\text{ m}\) (already in meters)
• \(1.0\text{ m}\) (already in meters)
• \(3.0\times10^{-7}\text{ m}\) (already in meters)
• \(4.0\times10^{3}\text{ mm}=4.0\times10^{3}\times10^{-3}\text{ m}=4.0\text{ m}\) (using \(1\text{ mm} = 10^{-3}\text{ m}\))

Step2: Compare the exponents of 10

• For \(3.0\times10^{-7}\text{ m}\), the exponent is \(-7\)
• For \(2.0\times10^{-6}\text{ m}\), the exponent is \(-6\)
• For \(1.0\times10^{-5}\text{ m}\), the exponent is \(-5\)
• For \(1.0\text{ m}=1.0\times10^{0}\text{ m}\), the exponent is \(0\)
• For \(4.0\text{ m}=4.0\times10^{0}\text{ m}\), the exponent is \(0\) (but coefficient \(4>1\))

Answer:

\(3.0\times10^{-7}\text{ m}<2.0\times10^{-6}\text{ m}<1.0\times10^{-5}\text{ m}<1.0\text{ m}<4.0\times10^{3}\text{ mm}\)