Identify which one of these are exact numbers. (Can be more than 1)
a. 2.54 cm ( the number of centimeters in exactly 1 in)
b. 56.00 s ( a time measured by a stopwatch)
c. 4 choices ( the number of choices in this list)
d. 3 lbs ( the weight of an object measured on a scale )
The Correct Answer and Explanation is:
The exact numbers in the given options are:
- a. 2.54 cm (the number of centimeters in exactly 1 in)
- c. 4 choices (the number of choices in this list)
Explanation:
An exact number is a value that is defined and does not have any uncertainty or measurement error. These are often based on counting or defined relationships that have no variability. Let’s analyze each option:
a. 2.54 cm (the number of centimeters in exactly 1 inch)
This is an exact number because the conversion between inches and centimeters is defined precisely. The relationship that 1 inch equals exactly 2.54 centimeters is a standard, universally accepted definition. There is no measurement error or approximation in this value; it is a defined constant.
b. 56.00 s (a time measured by a stopwatch)
This is not an exact number. Although the number 56.00 is precise, it comes from a measurement (from the stopwatch), and measurements always have some degree of uncertainty or error, even if it’s very small. The decimal places indicate precision, but the number is still subject to the limitations of the measuring device. Therefore, it is considered a measured number rather than an exact number.
c. 4 choices (the number of choices in this list)
This is an exact number because it represents a count of discrete items (choices). Counting is a process that results in exact numbers since there is no uncertainty when determining the number of objects or options. The number 4 is an exact count, not subject to variation.
d. 3 lbs (the weight of an object measured on a scale)
This is not an exact number. The weight of an object, measured on a scale, involves a measurement and is therefore subject to uncertainty, depending on the accuracy of the scale. Even if the weight reads 3 lbs, slight variations or errors in the measuring instrument could exist, making it a measured number rather than an exact number.
Conclusion:
The exact numbers in this list are:
- a. 2.54 cm
- c. 4 choices