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Problem 1 Solution

There are 365.25 days in a year and exactly 1440 minutes in a day. How many significant digits are in 365.25? How many are in 1440?

365.25 has 5 significant digits,  1440. has 4 significant digits

Solution Steps for Problem 1

The key: Remember the definition of significant digits. When a number is reported, the decimal point matters, but "place holding zeros" do not count.

In the first case, there are clearly 5 significant digits.

In the second case, since the number is followed by a decimal point, that means that the 0 in the units place is significant. Plus you know that there are 24 * 60 minutes exactly in a day by definition, so there are exactly 1440. minutes, and you can be sure that this is a counting number, not a measurement.

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