Question

"Determine whether the following statement is always, sometimes, or never true. Give examples to justify your answer.

The product of two decimals less than 1 is less than either of the factors."


Please help me....

Answer 1

Always true. Even if you multiply 0.9999999x0.9999999=0.99999980000001 it's still smaller than both of the factors.

Answer 2

The following statement is always true.

Explanation:

Consider the provided statement.

"The product of two decimals less than 1 is less than either of the factors."

Lets verify this with the help of few examples

Multiplying 0.1 and 0.5

0.1×0.5=0.05

0.005 is less than 0.1 as well as 0.5

Now consider another example:

0.4×0.9=0.36

0.36 is less than 0.4 as well as 0.9

Multiplying 0.99999 and 0.99999999

0.99999×0.99999999=0.9999899900001

0.9999899900001 is less than 0.99999 as well as 0.99999999

Hence, the following statement is always true.