For measuring some basic units like distance, weight, and liquid capacity, there are two main systems that are used. The first one is customary or standard units of measurement and the other is the metric system. Customary units of measure includes, inches, feet and miles which are used for the distance, and ounces, pounds, and tons which are used for measuring the weight. And the metric system is inclusive of the meters and kilometers for measuring the distance between two points, and grams and kilograms for finding the weight.

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In this system, units of measure are the multiples of 10, 100, and 1000. In other words, metric units of measure are based on decimals. Here, the meter is the basic unit of measurement. A meter is a little longer than one yard. The basic unit of liquid measure is the liter. A liter is about the same size as a quart. The basic unit of weight is the gram. A gram is used to find small weight such as the weight of tablets. A kilogram is the metric unit which is used to measure people’s weight.

The following are used in metric measurements.

Kilo- | Hecto- | Deca- | Base unit | Deci- | Centi- | Milli- |

1000x | 100x | 10x | liter meter gram | 0.1x | 0.01x | 0.001x |

The chart of the metric units of measure is as follows:

To change from one unit to another, we just have to move the decimal point.

The following figures also show the Density: Amount of mass per unit volume of a substance.

Customary Units of Measure | ||

Measures of Length | ||

1 foot (ft) | = | 12 inches (in.) |

1 yard (yd) | = | 36 inches |

1 yard (yd) | = | 3 feet |

1 mile (mi) | = | 5280 feet |

1 mile (mi) | = | 1760 yards |

Measures of Weight | ||

1 pound (lb) | = | 16 ounces (oz) |

1 ton (T) | = | 2000 pounds |

Liquid Measures | ||

1 pint (pt) | = | 16 ounces (oz) |

1 cup | = | 8 ounces |

1 pint | = | 2 cups |

1 gallon (gal) | = | 4 quarts |

1 quart (qt) | = | 2 pints |

Measures of Time | ||

1 minute (min) | = | 60 seconds (sec) |

1 hour (hr) | = | 60 minutes |

1 day | = | 24 hours |

1 week (wk) | = | 7 days |

1 years (yr) | = | 365 days / 366 days |

We use proportion to change one unit of measure to another. Remember that the parts of a proportion must correspond.

Units of Length | |

1 inch = 2.54 centimeters | 1 centimeter = 0.3937 inches |

1 foot = 0.3048 meters | 1 meter = 39.37 inches |

1 mile $\approx$ 1.6 kilometers | 1 kilometer $\approx$ 0.62 miles |

Units of Weight | |

1 pound $\approx$ 0.453 kilograms | 1 kilogram $\approx$ 2.2 pounds |

A ruler is a geometrical tool meant basically to measure short distances. Ideally under conventional measures, the rulers are marked in inches, centimeters or even feet.

There are specific rulers which use metric measures, and in such rulers the distances are marked in centimeters and meters.

Moreover, the gauges are measuring tools mainly used for finding mileage, temperature of materials, speed of vehicle, electrical flow of current, blood pressure of human system, etc.

Inch lines are the longest lines on the above ruler which are numbered as 1, 2 and so on. To read a length on a ruler we have to measure how far a point is to the right of zero.

The diagram below shows the dial of an instrument that measures amperes. An ampere is a unit of electric current. The dial is labeled from 0 to 50 with a small mark halfway between each number.

Example 1:

Solution: