Rational and Irrational Numbers Practice
Math 8 Q1 (Pre-Algebra) / The Number System
Which of the following is a rational number: 2π, 60, 61−−√, or 0.37815?(1 point)
The rational numbers are numbers that can be expressed as a fraction or a ratio of two integers.
Out of the given options, 60 and 0.37815 can both be expressed as fractions.
60 can be expressed as 60/1, so it is a rational number.
0.37815 can be expressed as 37815/100000, which can be simplified to 7563/20000, making it a rational number as well.
Therefore, the answer is 60 and 0.37815.
Rational and Irrational Numbers Practice
Math 8 Q1 (Pre-Algebra) / The Number System
Which of the following is an irrational number: −1529, 0.343434..., 2√3, or 87.9821?(1 point)
An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers.
Out of the given options, 0.343434... and 2√3 are both irrational numbers.
0.343434... is a repeating decimal, and it does not terminate or repeat in a pattern, making it irrational.
2√3 represents the product of 2 and the square root of 3. The square root of 3 is an irrational number, and multiplying it by 2 does not change its irrationality. Therefore, 2√3 is also an irrational number.
Therefore, the answer is 0.343434... and 2√3.
which one is it?
Apologies for the confusion. The correct answer is 0.343434... and 2√3.
Rational and Irrational Numbers Practice
Math 8 Q1 (Pre-Algebra) / The Number System
Which of the following is a rational number: 32−−√, 81−−√, 90−−√, or 125−−−√?(1 point)
To determine if a number is rational or irrational, we need to check if it can be expressed as a fraction or a ratio of two integers.
Out of the given options, 32−−√ and 81−−√ are both rational numbers.
32−−√ can be expressed as the square root of 32. Simplifying this radical, we find that √32 = √(16*2) = √16 * √2 = 4√2. Since 4√2 can be expressed as a fraction (4√2/1), 32−−√ is a rational number.
Similarly, 81−−√ can be expressed as the square root of 81, which is 9. Since 9 can be expressed as 9/1, 81−−√ is also a rational number.
On the other hand, 90−−√ and 125−−−√ cannot be expressed as the square root of a perfect square, and thus cannot be simplified or written as a fraction. These numbers are irrational.
Therefore, the answer is 32−−√ and 81−−√.
there can only be 1 answer
Apologies for the misunderstanding. The correct answer is 81−−√.
The square root of 81 is 9, which can be expressed as a fraction (9/1), making it a rational number.
32−−√, 90−−√, and 125−−−√ cannot be simplified or written as a fraction, so they are irrational numbers.
Therefore, the only rational number out of the given options is 81−−√.
To determine which of the given numbers is rational, we need to understand the definition of rational numbers. Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero.
Now let's consider each given number:
1. 2π: This is not a rational number because π (pi) is an irrational number. Irrational numbers cannot be expressed as a fraction of two integers.
2. 60: This is a rational number. It can be expressed as 60/1, where both 60 and 1 are integers.
3. 61√: This is also not a rational number because √61 is an irrational number. Just like with π, irrational numbers cannot be expressed as a fraction of two integers.
4. 0.37815: This is a rational number. It can be expressed as a fraction by multiplying both the numerator and denominator by a power of 10 to eliminate the decimal places.
Therefore, the only rational number among the given options is 60.