91Ó°ÊÓ

Explain why measurement standards based on laboratory procedures are preferable to those based on specific objects such as the international prototype kilogram.

When a computer that carries seven significant figures adds 1.000000 and \(2.5 \times 10^{-15},\) what's its answer? Why?

Why doesn't Earth's rotation provide a suitable time standard?

To raise a power of 10 to another power, you multiply the exponent by the power. Explain why this works.

What facts might a scientist use in estimating Earth's age?

How would you determine the length of a curved line?

Write \(1 / x\) as \(x\) to some power.

Emissions of carbon dioxide from fossil-fuel combustion are often expressed in gigatonnes per year, where 1 tonne \(=1000 \mathrm{kg}\). But sometimes \(\mathrm{CO}_{2}\) emissions are given in petagrams per year. How are the two units related?

In Chapter \(3,\) you'll learn that the range of a projectile launched -over level ground is given by \(x=v_{0}^{2} \sin 2 \theta / g,\) where \(v_{0}\) is the inimial speed, \(\theta\) is the launch angle, and \(g\) is the acceleration of gravIty. If you did an experiment that involved launching projectiles -with the same speed \(v_{0}\) but different launch angles, what quantity \- would you plot the range \(x\) against in order to get a straight line and thus verify this relationship?

What is meant by an explicit-constant definition of a unit?