Question

00:00Drag a tile to each number to classify it as rational or irrational.rationalirrational9.682.010010001...✓ 64-51/5✓ 6

Answer 1

To classify each number as a rational or irrational number, first we need to define what a rational and irrational number is.

Rational numbers: are the ones that can be written in a fraction form, and that have periodic decimals (can be infinite decimals but they have to have a sequence to them).

Irrational number: are the ones that have infinite and non-periodic decimals (the decimals don't have a defined sequence)

Let's analyze each case.

$9.68^-$

The bar on top of the number 8 represent that the number 8 repeats itself:

$9.6888888\ldots$

This decimals are infinite but they are periodic, which means that we have a defined sequence in this decimals (it will always follow the number 8). Thus, this is a rational number.

For the second number:

$2.010010001\ldots$

Since there is no sequence in the decimals in this case, this is an irrational number.

For the third number:

$\sqrt[\square]{64}$

The square root of 64 is equal to 8:

$\sqrt[]{64}=8$

and all the whole or integer numbers are also rational.

For the fourth number:

$-\frac{51}{5}$

This is a rational number, because as we can see, it is represented in a decimal form which is a property of rational numbers.

For the last number:

$\sqrt[\square]{6}$

and since this square root is not exact as the square root of option 3, this is an irrational number because:

$\sqrt[\square]{6}=2.4494897\ldots$

Which are non-periodic decimals (without a defined sequence).