# 1.2: Metric System Prefixes and the Metric Ladder

- Page ID
- 24123

Prefix | Fraction | Decimal | Scientific Notation |

nano (n) = 1 billionth | 1/1,000,000,000 | 0.000000001 | 10^{-9} |

micro () = 1 millionth | 1/1,000,000 | 0.000001 | 10^{-6} |

milli (m) = 1 thousandth | 1/1,000 | 0.001 | 10^{–3} |

centi(c) = 1 hundredth | 1/100 | 0.01 | 10^{-2} |

kilo (k) = 1 thousand | 1000 | 1000 | 10^{3} |

Remember

- The metric system is based on units of 10. Count zeros. Consult the metric ladder as to how many spaces to move the decimal point.
- Move the decimal left when converting from a smaller to larger value (DIVIDE)
- Move the decimal right when converting from a larger to smaller value (MULTIPLY)

Example \(\PageIndex{1}\)

One meter is how many kilometers? The question involves going from a smaller value (meter) to a larger value (kilometer). Move the decimal to the left (divide)

**Solution**

1.0 meter = .001 kilometers = 1 X 10^{-3} kilometers

Example \(\PageIndex{2}\)

How many millimeters are in 5 meters? The question involves going from a larger value (meters) to a smaller value (millimeters). Move 3 decimal places to the right (multiply).

**Solution**

5.0 meters = 5000 millimeters = 5 X 10^{3} millimeters

Example \(\PageIndex{3}\)

How many liters are in 80 nanoliters? The question involves converting a small value (nanoliters) to a larger value (liters). Move the decimal to the left 9 places

**Solution**

80. nanoliters = .00000008 liters = 8 X 10^{-8 }liters