Question

Which statement about the product is true?? 7.56 x 6.777777...

A:The product is irrational.
B:The product is rational.
C:The product is neither rational nor irrational.
D:The nature of the product cannont be determined.

Answer 1

b. because 6.7777... is a repeating decimal with a pattern which means it can be turned into a fraction. if it was a repeating decimal with no pattern like π then it would be irrational.

Answer 2

Answer: The correct answer is Option B.

Explanation:

The given numbers are: 7.56 and 6.777777.....

Both the numbers are rational as they can be expressed in the form of
`(p)/(q)` where
`q\\eq 0`

• Expressing 7.56 in fractional form:

`\Rightarrow 7.56=(756)/(100)`

• Expressing 6.777777.... in fractional form:

`x=6.77777.........` .......(1)

Multiplying both the sides of equation by 10, we get:

`10x=67.77777.....` ........(2)

Now, subtracting equation 2 from equation 1, we get:

`9x=61\\\\x=(61)/(9)`

The multiplication of two rational numbers, will always produce a rational number.

`\Rightarrow (756)/(100)* (61)/(9)=(1281)/(25)=51.24`

Hence, the correct answer is Option B.