Free Math Worksheets

- Express each metric prefix as a power of \(10\). - Move the decimal point until the coefficient is at least \(1\) and less than \(10\). - Adjust the exponent to compensate for the decimal shift.

1. Since \(1\,\text{mm}=10^{-3}\,\text{m}\), \(0.25\,\text{mm}=0.25\times10^{-3}\,\text{m}=2.5\times10^{-4}\,\text{m}\). 2. Since \(1\,\mu\text{m}=10^{-6}\,\text{m}\), \(2\,\mu\text{m}=2\times10^{-6}\,\text{m}\). 3. Since \(1\,\text{nm}=10^{-9}\,\text{m}\), \(25\,\text{nm}=25\times10^{-9}\,\text{m}=2.5\times10^{-8}\,\text{m}\).

a) \(2.5\times10^{-4}\,\text{m}\) b) \(2\times10^{-6}\,\text{m}\) c) \(2.5\times10^{-8}\,\text{m}\)

- Use the order \(\text{mm}^3\), \(\text{cm}^3\), \(\text{dm}^3\), \(\text{m}^3\). - Adjacent cubic metric units differ by a factor of \(10^3\). - Liters are equivalent to cubic decimeters.

1. For part a, \(2.4\times10^3\,\text{cm}^3=2400\,\text{cm}^3\). In cubic millimeters, this is \(2.4\times10^6\,\text{mm}^3\). In cubic decimeters, it is \(2.4\,\text{dm}^3\). 2. For part b, \(0.05\,\text{dm}^3=50\,\text{cm}^3\). In cubic meters, it is \(5\times10^{-5}\,\text{m}^3\). 3. For part c, treat \(7.1\,\text{L}\) as \(7.1\,\text{dm}^3\). In cubic centimeters, it is \(7100\,\text{cm}^3\). In cubic meters, it is \(0.0071\,\text{m}^3\).

a) Smaller: \(2.4\times10^6\,\text{mm}^3\); larger: \(2.4\,\text{dm}^3\) b) Smaller: \(50\,\text{cm}^3\); larger: \(5\times10^{-5}\,\text{m}^3\) c) Smaller: \(7100\,\text{cm}^3\); larger: \(0.0071\,\text{m}^3\)