Which of the following are exact numbers?
a. There are 100 cm in 1 m.
b. One meter equals 1.094 yard.
c. We can use the equation:
F=9/5 C + 32
to convert from Celsius to Fahrenheit
temperature. Are the numbers 9/5 and 32
exact or inexact?
d. π
a exact. c. they are exact
To determine which of the following are exact numbers, let's analyze each option:
a. There are 100 cm in 1 m.
This statement is an exact conversion factor, as it represents a defined relationship between centimeters and meters.
b. One meter equals 1.094 yard.
This statement is an approximation because the conversion factor between meters and yards is not an exact whole number.
c. We can use the equation: F=9/5 C + 32 to convert from Celsius to Fahrenheit temperature. Are the numbers 9/5 and 32 exact or inexact?
In this equation, the numbers 9/5 and 32 are exact. The fraction 9/5 can also be expressed as 1.8, which is an exact number. Similarly, the value 32 is an exact number.
d. π
The value of π (pi) is an irrational number, which means it cannot be expressed as a precise fraction or decimal. Hence, it is not an exact number.
So, the exact numbers in the given options are:
- 100 cm in 1 m.
- The numbers 9/5 and 32 in the equation F=9/5 C + 32.
To determine which of the given options are exact numbers, we need to understand what an exact number is.
An exact number is a value that is known with complete certainty and does not involve any measurement or estimation. These values are typically derived from definitions or relationships between quantities.
Now let's analyze each option:
a. "There are 100 cm in 1 m." - This statement represents an exact relationship, as it is a defined conversion between centimeters and meters. Therefore, this is an exact number.
b. "One meter equals 1.094 yard." - This statement is also an exact relationship, as it is a defined conversion between meters and yards. Thus, this is an exact number as well.
c. "We can use the equation: F = (9/5)C + 32 to convert from Celsius to Fahrenheit temperature. Are the numbers 9/5 and 32 exact or inexact?" - In this equation, the numbers 9/5 and 32 are exact values. The fraction 9/5 represents the exact conversion factor between Celsius and Fahrenheit. The number 32 is the exact value used to shift the temperature scale. Therefore, both 9/5 and 32 are exact numbers.
d. "π" - The value π (pi) represents the ratio of the circumference of a circle to its diameter. It is an irrational number, meaning that it cannot be expressed as a finite fraction or a terminating or repeating decimal. Since it is not an exact value and involves an approximation, π is not an exact number.
In summary, the exact numbers in the given options are:
a. 100
b. 1.094
c. 9/5 and 32
The number π is not an exact number.