# Chapter 1 - Measurement - Problems - Page 9: 11b

The ratio of a French decimal second to the standard second can be expressed as any of the following: 125 : 108 1.1574 : 1 1 : 0.864

#### Work Step by Step

There is some information left out of the problem, and that is the fact that the French decimal day is equivalent in time to the standard day. You must use this equality to solve the problem. You can find out, using dimensional analysis, how many seconds are in the French decimal day, and take the ratio of that to how many seconds are in the standard day. French Decimal Seconds in a Day 100 $\frac{seconds}{minute}$ * 100 $\frac{minutes}{hour}$ * 10 $\frac{hours}{day}$ = 100,000 $\frac{seconds}{day}$ Standard Seconds in a Day 60 $\frac{seconds}{minute}$ * 60 $\frac{minutes}{hour}$ * 24 $\frac{hours}{day}$ = 86,400 $\frac{seconds}{day}$ Thus the Ratio of French Decimal Seconds to Standard Seconds is 100,000 : 86,400 800 can be factored out, and the ratio can be further simplified to 125 : 108

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