Without Computing, decide whether the value of each expression is much smaller than one, close to one, or much greater than one.

a. Much smaller than 1. This is because the numerator (100) is much smaller than the denominator (1000)

b. Close to one. The numerator and denominator are fairly close in value only a difference of 1/3 - 1/4 = 4/12-3/12 = 1/12 = 0.0833

c. Close to one. The values 4.7 and 5.2 are fairly close to one another, so dividing them should lead to some value smaller than 1 but fairly close to it.

d. Much smaller than 1. The numerator is much smaller than the denominator.

e. Much larger than 1. This is the reverse of choice D above

f. Much smaller than 1. Think of 0.002 as 2/1000. So we really have 2/1000 divided by 2000 = (2/1000)*(1/2000) = 2/(2,000,000) = 1/(1,000,000).