Is 2.34 a rational number? Show your work and explain your answer.
My answer: Yes, 2.34 is a rational number because if i convert it into a fraction, I will get 2 and 17/50 and any decimal or integer counts as a decimal.
correct in principle, but technically, 2 17/50 is a mixed number. Its fractional equivalent is 117/50
Yes it is 2.34 can be written as a fraction. Rational can be written as a fraction and irrational cant be. Pi would be considered irrational because it goes on forever.
Well, well, well, if it isn't our old friend 2.34. Let's investigate if this numero is rational, shall we?
To determine if a number is rational, we need to see if we can express it as a fraction. So, let's get down to business!
To convert 2.34 into a fraction, we need to tackle the decimal part first. Since there are two decimal places, we can multiply 2.34 by 100 to get rid of those pesky dots. Voila, we have 234.
Now we need to put that 234 over the appropriate power of 10. Again, because of the two decimal places, we use 100. So, we have 234/100.
But don't celebrate just yet, we can still simplify this fraction. Dividing both the numerator and denominator by 2, we get 117/50.
And there you have it! 2.34 can be expressed as a fraction, specifically, 117/50. So, my comedic companion, 2.34 is indeed a rational number. Enjoy the numerical party!
To determine if 2.34 is a rational number, we need to check if it can be expressed as a fraction of two integers.
To convert the decimal 2.34 to a fraction, we follow these steps:
1. Note that there are two digits after the decimal point. Therefore, we can consider 2.34 as a number with two decimal places.
2. We multiply 2.34 by a power of 10 to move the decimal places to the right. In this case, we multiply by 100 to remove the decimal places.
2.34 * 100 = 234
3. The resulting number, 234, is an integer. Thus, the decimal 2.34 can be expressed as the fraction 234/100.
4. Next, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).
GCD(234, 100) = 2
234/100 = (234 ÷ 2) / (100 ÷ 2) = 117/50
Therefore, 2.34 is indeed a rational number because it can be expressed as the fraction 117/50, where both the numerator and denominator are integers.