If its decimal representation is either terminating or a repeating number then it is rational. Otherwise it is irrational.
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No. An irratioinal number is a number that cannot be expressed as a fraction 6.23 = 623/1000 (you can check this on your calculator, if you'd like). The existence of this fraction means, by the definition given above, the 6.23 is not an irrational number. In more applied terms, any number with a decimal without repeating terms is ALWAYS rational. In decimals with repeating terms, as long as the terms follow some pattern, the number is rational. example: 0.3333333333... is rational because the numbers follow a pattern (and because this = 1/3). pi (or 3.141592.....) is not rational because the numbers do not follow a pattern.
You keep the first digit, replace the remaining digits with zero, and check whether you need to round the first digit up or not.
1. First we need to determine the least common denominator of the fractions in the given rational equation. 2. We need to take out the fractions by multiplying All terms by the least common denominator. 3. Then we have to simplify the terms in rational equation. 4. Solve the resulting equation. 5. Check the answers to make confident the solution does not make the fraction undefined.
I don't see any numbers below.One method to solve this is to replace each of the numbers in the inequality, do the calculations, and then check whether the inequality is satisfied. Another method is to get the general solution for the inequality, then check with each of the numbers.
The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.
please rephrase or grammar-check your question.
There is no simple method. If you can write the number as a ratio of two integers, in the form p/q where q>0, then the number is rational. But it is often very difficult to show that such a representation is not possible.
No. An irratioinal number is a number that cannot be expressed as a fraction 6.23 = 623/1000 (you can check this on your calculator, if you'd like). The existence of this fraction means, by the definition given above, the 6.23 is not an irrational number. In more applied terms, any number with a decimal without repeating terms is ALWAYS rational. In decimals with repeating terms, as long as the terms follow some pattern, the number is rational. example: 0.3333333333... is rational because the numbers follow a pattern (and because this = 1/3). pi (or 3.141592.....) is not rational because the numbers do not follow a pattern.
A rational, non-zero number multiplied by an irrational number always results in an irrational number. Knowing this, you can fairly easily choose a rational number to multiply by any given irrational that will be within your stated range. In this example, I'm going to choose pi (~3.1415926535897932) as the irrational number and x will be the rational number. So we want to satisfying the following inequality: 0.6 < pi * x < 0.66 Dividing everything by pi (which is positive) gives us: 0.6/pi < x < 0.66/pi A quick check on the calculator tells us that: 0.6/pi ~= 0.191 0.66/pi ~= 0.21 So, choosing x = 0.20, we end up with 0.2 * pi as our answer. A quick verification with the calculator shows that 0.2 * pi ~= 0.628, so it's between 0.6 and 0.66. Since 0.2 is 1/5, the equivalent pi/5 is a slightly more aesthetic answer.
1). This isn't a mathematical proof or definition, but it turns out that any numberthat you can completely write with digits is rational. We will now attempt to write121 completely, using digits:121We did it! So we're pretty sure that 121 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 121 as the ratio of two whole numbers:121/1Again, we've succeeded! So 121 is definitely a rational number.
You should check whether you can simplify the answer.
45
A rational number is one that can be expressed as a ratio of two integers. In this case, 4.46466 is a decimal number and not a whole number. To determine if it is rational, we can check if it can be expressed as a fraction. If we convert 4.46466 to a fraction, we find that it can be expressed as 446466/100000, which simplifies to 223233/50000. Therefore, 4.46466 is a rational number.
1). Quick check: Any number that you can write down completely with digits is a rational number. So yes, it is. 2). Formal analysis: A rational number is a number that can be written as the ratio of two integers. 375 is the ratio of 375 to 1 ( 375/1 ) . So yes, it is.
if it's square root is an integer, it is a square number.
An irrational number is a number which cannot be expressed as a fraction made of integers. These numbers generally have infinite decimals with no pattern to them whatsoever. The easiest way, I think, to make an irrational number is to take the square root of a number between the squares of your parameters, in this case between 2500 and 4900. Thus a number such as square root(2738), which is 52.325901..., or square root(4677), which is 68.388595..., will do nicely. In this case make sure you check your answer because some numbers such as 3600 will lead to whole number (and non-irrational) answers.