Question

57. In each of the sets below, choose the one quantity or number which is exact.

a. i. the human population
ii. the distance in light years from the sun to Alpha Centauri, a nearby star
iii. the winning time for the 100 m dash in the Olympic Games

b. i. the weight of a particular one cent coin in g
ii. the boiling point of lead, in °C
iii. the number of cm in 1 yd

c. i. the measured value of the speed of light (2.998... × 108 m/s)
ii. π (3.141...)
iii. the volume of milk in a 1-gallon jug

Answer 1

In the given sets, the exact quantities are the winning time for the 100 m dash in the Olympic Games, the number of cm in 1 yard, and the constant π (pi). Exact numbers are defined or recorded precisely and don't change or require measurement.

Step-by-step explanation:

To answer the question of which quantity or number is exact in each set, we need to understand that an exact number is one that is defined and does not change or require measurement. Let's examine each set:

• Set a: The only exact quantity here is the winning time for the 100 m dash in the Olympic Games because it is recorded to a precise value that doesn't change once the race is over.
• Set b: The number of cm in 1 yard is an exact quantity because it is defined as 91.44 cm exactly.
• Set c: Here, π (3.141...) is the exact number despite being an irrational number because its value is constant and does not vary.

Now, let's explore each of these further:

• a. Choosing the winning time for a 100 m dash in the Olympic Games is exact because once the official time is recorded, it doesn't change, whereas the human population and the distance to Alpha Centauri are subject to measurement and not defined by exact values.
• b. One yard is always exactly 91.44 centimeters, and this measurement is based on definition. Therefore, it eliminates uncertainty and does not need to be measured.
• c. Although we normally use approximations for π in calculations, its value is exact and not subject to