1). This isn't a mathematical proof or definition, but it turns out that any number
that you can completely write with digits is rational. We will now attempt to write
2.7 completely, using digits:
2.7We did it! So we're pretty sure that 2.7 is probably a rational number.Now we'll check it out according to the official mathematical definition:
2). "A rational number is any number that can be written as the ratio of two whole numbers."
We will now attempt to write 2.7 as the ratio of two whole numbers:
27/10Again, we've succeeded! So 2.7 is definitely a rational number.No, the square root of 27 is not a rational number. A rational number is a number that can be expressed as a fraction where both the numerator and denominator are integers. The square root of 27 is an irrational number because it cannot be expressed as a simple fraction and its decimal representation goes on indefinitely without repeating.
yes
Yes.
It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
yes
No, it is rational.
Yes, 27 is a real number. Real numbers include all rational and irrational numbers, and 27 is a rational number because it can be expressed as a fraction, 27/1.
No. 27 is a whole number, and all whole numbers are rational.
No.
No, the square root of 27 is not a rational number. A rational number is a number that can be expressed as a fraction where both the numerator and denominator are integers. The square root of 27 is an irrational number because it cannot be expressed as a simple fraction and its decimal representation goes on indefinitely without repeating.
If you can completely write a number, using digits, fractions and decimals, then the number is rational. You appear to have done that.
Yes.
30
If you can completely write a number, using digits, fractions and decimals, then the number is rational. You appear to have accomplished that.
The square root of 729 is 27.Yes, it is a rational number because 27 can be written as simple fraction, 27/1.
There are infinitely many rational numbers between 2 and 27.
5.4 = 5 2/5 = 27/5 so it is a rational number.