Question

Which of these statements about uncertain and exact numbers are TRUE?

I) In the phrase "gas mileage is 27 miles/gallon", 27 is exact because it is an integer
II) Numbers with decimal places cannot be exact
III) Numbers that are measured cannot be exact
IV) The conversion "1 mile = 1.6093447 km" is exact because it shows 8 significant figures

Answer 1

In uncertain and exact numbers, the statement I is true, statement II is false, statement III is true, and statement IV is true.

Step-by-step explanation:

When it comes to uncertain and exact numbers, there are a few statements that are true:

1. The statement I) is true. In the phrase 'gas mileage is 27 miles/gallon', 27 is an exact number because it is an integer. Exact numbers can be whole numbers or those derived from definitions or counted objects.
2. The statement II) is false. Numbers with decimal places can be exact if they are derived from definitions or counted objects. For example, 1 inch is exactly 2.54 centimeters.
3. The statement III) is true. Numbers that are measured are uncertain because there is always some degree of variability in measurement. For example, if you measure the length of a pencil, there may be small variations due to the measuring instrument or other factors.
4. The statement IV) is true. The conversion '1 mile = 1.6093447 km' is exact because it is a derived from a definition. It shows 8 significant figures, indicating the precision of the conversion factor.