Irrational Numbers

The fraction 12/18 can be simplified to 2/3 by dividing both the numerator and denominator by their greatest common divisor, which is 6. Since the fraction 2/3 can be expressed as a ratio of two integers and can be written in the form a/b where a and b are integers and b is not equal to 0, it is considered a rational number. Rational numbers are numbers that can be expressed as a ratio of two integers.

Oh, absolutely! 0.025 is a rational number because it can be expressed as a fraction, in this case, 25/100. Remember, rational numbers can be written as a ratio of two integers, and 0.025 fits that definition perfectly. Just like happy little trees, rational numbers can be found all around us in the world of math.

7.5

15.77 is a rational number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. In this case, 15.77 can be written as 1577/100, which meets the criteria for a rational number.

The number 5.123 is rational. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. In this case, 5.123 can be expressed as the fraction 5123/1000, where both the numerator (5123) and the denominator (1000) are integers.

9 out of 7 is a rational number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers, and the denominator is not zero. In this case, 9/7 can be simplified to 1.28571428571, which is a rational number.

5.2

These appear in decimal representations AFTER the decimal point. The two dots indicate the start and end of a string of numbers that should be repeated infinitely to get an exact decimal equivalent. If there is only one digit to be repeated, the two dots are replace by one.

For example,

1/11 = 0.090909 and on and on forever. This can be written with a dot over a 0 and and 9. I can't do that here but will put a dot superscript just after the digit, thus:

1/11 = 0.09.0. or 0.0.9.

or, for a longer repeating string, 9/7 = 1.285714285714....

= 1.2.85714.

No.

-67 is a rational number

Any number that can be represented as a ratio of two integers is rational. Those that cannot are irrational.

Since -67 can be represented as the ratio -67/1 (both -67 and 1 are integers) it is rational.

Well, isn't that just a happy little question! The value of the square root of 2 is approximately 1.414. It's a special number that shows up in nature and mathematics, like a little gift from the universe. Just remember, every number is unique and adds its own special touch to the world around us.

3.1415 is rational (as are all other terminating decimals). Note that these are some of the first few digits of pi (3.14159…, which really should be rounded to 3.1416 not 5); pi is an irrational number. Approximations of pi are generally rational numbers.

The number -3 is a rational number. A rational number is any number that can be expressed as a fraction where the numerator and denominator are integers and the denominator is not zero. In this case, -3 can be expressed as the fraction -3/1. Since -3 can be expressed as a ratio of two integers, it is considered a rational number.

4.8

-52 is a rational number because it can be expressed as a fraction in the form of -52/1

rational

Well, honey, the square root of zero is actually just zero. And guess what? Zero is as rational as it gets in the number world. So, yes, the square root of zero is a rational number. But hey, don't sweat it if math isn't your thing, we can't all be numbers wizards.

Yes, unlike pi it either cancels out or there is a defined pattern such as the 6's

The number 0.424242... is rational. A rational number is one that can be expressed as a ratio of two integers, where the denominator is not zero. In this case, the repeating decimal 0.424242... can be expressed as the fraction 14/33, making it a rational number.

Well, isn't that a happy little question! 0.21 is a rational number because it can be expressed as a fraction, specifically 21/100. Just like painting a beautiful landscape, math can be a lovely and calming experience once you understand its gentle rhythms.

An irrational number is a real number that cannot be expressed as a simple fraction, meaning it cannot be written as a ratio of two integers. These numbers have non-repeating, non-terminating decimal representations. Examples of irrational numbers include the square root of 2, pi, and the golden ratio. They are contrasted with rational numbers, which can be expressed as fractions.

Actually, a repeating decimal is not necessarily an irrational number. A repeating decimal is a decimal number that has a repeating pattern of digits after the decimal point. While some repeating decimals can be irrational, such as 0.1010010001..., others can be rational, like 0.3333... which is equal to 1/3. Irrational numbers are numbers that cannot be expressed as a simple fraction, and they have non-repeating, non-terminating decimal representations.

I would say no, it is rational. A number is only irrational if it repeats with no specific pattern.

No. 2 + sqrt(5) and 2 - sqrt(2) are both irrational but their sum, 4 is rational.

The number 2468 is a rational number. A rational number is any number that can be expressed as the ratio of two integers, where the denominator is not zero. In this case, 2468 can be expressed as the ratio 2468/1, which makes it a rational number.

Irrational numbers are denoted by the symbol "s" to distinguish them from rational numbers, which can be expressed as fractions. Irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal representations. The symbol "s" serves as a placeholder to represent these numbers in mathematical equations and calculations.