Which statement about the product 6.57 x 2.67534 is true? Show your work
a) the product is irrational
b) the product is rational
c) the product is neither rational nor irrational
d) The nature of the product cannot be determined.
To determine if the product 6.57 x 2.67534 is rational or irrational, we need to multiply these numbers and see if the result can be expressed as a fraction or as a terminating or repeating decimal.
6.57 * 2.67534 = 17.5736978
Since 17.5736978 is a terminating decimal (it has a finite number of decimal places), we can express it as a fraction. Therefore, the product is rational.
Therefore, the correct statement is:
b) the product is rational
To determine the nature of the product 6.57 x 2.67534, we need to check if the product is rational or irrational.
The product of two rational numbers is always rational. Therefore, if 6.57 and 2.67534 are rational numbers, their product will also be rational.
6.57 is a rational number because it can be expressed as a fraction: 657/100.
2.67534 is also a rational number because it can be expressed as a fraction: 267534/100000.
Now, we can calculate the product:
(657/100) x (267534/100000) = (657 x 267534) / (100 x 100000)
Simplifying further:
(657 x 267534) / (100 x 100000) = 175489938 / 10000000
This fraction can be further simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which in this case is 2.
Simplifying by dividing both by 2:
(175489938 ÷ 2) / (10000000 ÷ 2) = (87744969 / 5000000)
The fraction 87744969/5000000 is still a rational number since it can be expressed as a fraction.
Therefore, the statement "b) the product is rational" is true.