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Dimensional Analysis Part 2

Linear Measure | ||

2.54 cm | = | 1 in |

12 in | = | 1 ft |

5280 ft | = | 1 mi |

0.3048 m | = | 1 ft |

1 km | = | 0.621 mi |

1 furlong | = | 660 ft |

3 ft | = | 1 yd |

0.0394 in | = | 1 mm |

Weight/Mass | ||

1 stone | = | 14 lbs |

1 lb | = | 0.4536 kg |

1 oz | = | 16 drams |

1 oz | = | 28.3 g |

16 oz | = | 1 lb |

2,000 lbs | = | 1 ton |

1 oz | = | 28,350 mg |

1 carat | = | 0.2 g |

Volumetric Measure | ||

1 cup | = | 16 tablespoons |

2 cups | = | 1 pint |

2 pints | = | 1 quart |

1 gal | = | 4 quarts |

1 gal | = | 3.78 L |

1 mL | = | 1 cm^{3} |

1 m^{3} |
= | 1000 L |

1 cup | = | 236.6 mL |

Time | ||

1,000 ms | = | 1 s |

60 s | = | 1 min |

60 min | = | 1 hr |

24 hr | = | 1 day |

365 day | = | 1 yr |

14 days | = | 1 fortnight |

10 yr | = | 1 decade |

100 yr | = | 1 century |

Some traditional units are not given in decimal form when there are whole units and parts of units. For example, weights for babies and produce are often given in this form—6 lbs 12 oz—rather than this one—6.75 lbs. Write the answers to the following conversions using this convention, which is also used for time units. For example, 2.5 hours is 2 hours 30 minutes.

To convert 10 lbs 2.5 oz to a decimal expressed in pounds you convert the 2.5 oz to pounds and add the result to the 10 lbs.

14.64 lbs can be written using both pounds and ounces by converting just the 0.64 lbs to oz.

1 lb 2.5 oz × --------- = 0.156 lb So the result is 10.156 lb. 16 ozTo convert in the other direction works like this:

14.64 lbs can be written using both pounds and ounces by converting just the 0.64 lbs to oz.

16 oz 0.64 lb × --------- = 10.24 oz So the result is 14 lb 10.2 oz. 1 lb

- Convert 5 lb 2 oz to decimal pounds
- Convert 12 lb 15 oz to decimal pounds
- Convert 7.88 pounds to pounds and ounces
- Convert 19.27 pounds to pounds and ounces

- Convert 2.75 hours to hours and minutes
- Convert 1.32 hours to hours and minutes
- Convert 3 hours 42 minutes to decimal hours
- Convert 7 hours 19 minutes to decimal hours

One reason this is important is that it enables much quicker arithmetic. Try the following problems to see why. Show your work for each step of each calculation. Do not try to do it in your head!

- Add the following weights:

(3 lbs 3 oz) + (2 lbs 14 oz) - What is the total weight of 7 items that weigh 4 lbs 9 oz each?
- How many blocks of classes can fit into 5 hours if blocks are 1 hr 15 minutes long?
- Convert 5.3 kg to pounds and ounces.

- Convert 3 lb 7 oz to kg
- Add these weights: (2.8 lbs) + (5.9 lbs)
- What is the total weight of 9 items that weigh 4.25 pounds each?
- What is the total amount of time required for 3 classes that are 1.625 hours long?

Some questions you can use to apply your skills.

- Calculate the number of days and hours in 1 million (1,000,000 or 1 × 10
^{6}) seconds. - Are you older than a million seconds? Were you surprised?
- A billion is a number that is 1,000 times a million (1,000,000,000 or 1 × 10
^{9}). Calculate the number of years, months, and days in a billion seconds. - Why is it a bit silly for people to say ‘millions and billions’ when they’re talking about large numbers?