Determine if 0, point, 3, 4, 3, 7, 50.34375 is rational or irrational and give a reason for your answer
To determine if a number is rational or irrational, we need to determine if it can be expressed as a fraction (rational) or if it cannot be expressed as a fraction (irrational).
Let's analyze each number in the given sequence:
0: 0 is a rational number because it can be expressed as the ratio of 0/1.
Point ("."): A decimal point is not a number and not meaningful in this context.
3: 3 is a rational number because it can be expressed as the ratio of 3/1.
4: 4 is a rational number because it can be expressed as the ratio of 4/1.
3: 3 is a rational number because it can be expressed as the ratio of 3/1.
7: 7 is a rational number because it can be expressed as the ratio of 7/1.
50.34375: 50.34375 is a rational number because it can be expressed as the fraction 50 11/32.
Therefore, all the numbers given are rational numbers.
To determine whether a number is rational or irrational, we need to check if it can be written as a fraction of two integers or not.
The number in question is 50.34375.
To initially assess if it may be rational, we can observe that it terminates after decimal places. This suggests it might be rational.
We can represent 50.34375 as a fraction by putting the decimal places over the appropriate powers of 10.
50.34375 = 5034375 / (10^2) + 10^(-5)
Simplifying the fraction gives us:
50.34375 = 5034375 / 100000
Next, we can check whether the numerator and denominator of the fraction can be reduced further.
50.34375 cannot be simplified further because the numerator, 5034375, is not divisible by any factor of the denominator, 100000.
Therefore, 50.34375 can be expressed as a fraction, meaning it is rational.
To determine if a number is rational or irrational, we need to understand the definitions of these terms.
A rational number can be expressed as the quotient of two integers (where the denominator is not zero). In other words, it can be written as a fraction in the form a/b, where a and b are integers.
On the other hand, an irrational number cannot be expressed as a fraction of two integers. It usually has decimal representations that neither terminate nor repeat.
Now let's analyze the given number: 0, 0. point, 3, 4, 3, 7, 50.34375.
Since the number is given as a decimal representation, we need to check if it can be expressed as a fraction of two integers.
To do this, let's rewrite the given number as a fraction. Since the given number has a decimal part, we need to determine if it repeats or terminates.
0.34375 is a repeating decimal because it has a repeating pattern of 375. A repeating decimal can be represented as a fraction by using the pattern as the repeating part and putting it over the appropriate number of 9s. So, 0.34375 can be rewritten as 34375/100000.
Now, let's consider the entire given number: 0, 0. point, 3, 4, 3, 7, 50.34375.
We can write this number as a sum of these two parts: 0 and 0.34375.
0 = 0/1 (rational)
0.34375 = 34375/100000 (rational)
So, the entire given number can be expressed as the sum of two rational numbers:
0 + 0.34375 = 0/1 + 34375/100000
Since both parts of the given number can be expressed as fractions, the entire number is rational.
Therefore, the number 0, point, 3, 4, 3, 7, 50.34375 is rational.