1988 AMC 12 Problem 10

Question

In an experiment, a scientific constant

C

is determined to be

2.43865

with an error of at most

\pm0.00312.

The experimenter wishes to announce a value for

C

in which every digit is significant. That is, whatever

C

is, the announced value must be the correct result when

C

is rounded to that number of digits. The most accurate value the experimenter can announce for

C

is

2

2.4

2.43

2.44

2.439

Find the smallest and largest possible values of

C

Round both endpoints to increasing numbers of significant digits

The possible interval is

[2.43553,2.44177].

Every number in it rounds to

2.44

at three significant digits, but the endpoints round differently at four significant digits. Hence

2.44

is the most accurate guaranteed announcement.

Thus the correct answer is D.

Problem 10 in other years