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Exact numbers are values that are known with complete certainty. They are not derived from measurements but from counting or defined relations. For instance, if you have '3 hamburgers,' this is an exact number.

Exact numbers often come from:

• Counting objects (e.g., 4 chairs, 2 dogs)
• Defined values (e.g., 1 dozen = 12 items, 1000 grams = 1 kilogram)
• Mathematical constants (e.g., 饾湅, defined conversion factors like 1 min = 60 s)

Since these numbers do not involve any form of estimation or measurement, they are precise and carry an infinite number of significant figures. For example, in pair d from the exercise, '60 s = 1 min,' both the seconds and minutes are defined and exact numbers.

Measured numbers are obtained through measurement using instruments. These values are approximations and carry a degree of uncertainty. For instance, '6 oz of hamburger' involves measuring the weight of the hamburger, which is why it's a measured number.

Measured numbers are often associated with:

• Physical quantities (e.g., weight, length, volume)
• Units of measurement (e.g., grams, liters, meters)

Whenever you measure something, you often use devices that come with their precision limits, adding some degree of uncertainty. In pair c from the exercise, both '0.75 lb of grapes' and '350 g of butter' are measured numbers because they are derived from measurements of mass.

Units of measurement are standardized quantities used to quantify and express physical attributes like length, mass, and volume. They provide a reference so that measurements are accurate and consistent. Examples include grams (g), liters (L), and meters (m).

Units serve a critical role by ensuring that measured numbers convey precise and understandable information. When dealing with '0.75 lb of grapes,' the 'lb' (pounds) is the unit of measurement that quantifies weight.

Some key points about units of measurement:

• International System of Units (SI) provides standard base units (e.g., meter for length, kilogram for mass)
• Units can be converted from one type to another using conversion factors
• Accuracy in using appropriate units is essential for scientific and everyday measurements

Hence, units of measurement are indispensable for interpreting measured numbers correctly.

Conversion factors are numerical values used to convert a measurement from one unit to another without changing its value. They form the bridge between different units and ensure accurate conversions. For example, converting minutes to seconds involves the conversion factor '60 s = 1 min.'

Conversion factors are vital in:

• Scientific calculations (e.g., converting milliliters to liters)
• Everyday measurements (e.g., inches to centimeters)
• Ensuring standardized and consistent measurements

They are often considered exact numbers because they are established and defined precisely. In pair d from the exercise, the relationship between seconds and minutes uses an exact conversion factor, making '60 s = 1 min' an exact number.

By understanding and using conversion factors correctly, you can seamlessly switch between different units of measurement while maintaining accuracy in your calculations.