Why is .3 repeating a rational number

Mathematics

2 answers:

s2008m [1.1K]3 years ago

5 0

Answer:

.333333... can be expressed as 1/3.

Step-by-step explanation:

A rational number is defined as:

any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

aka, any number that you can express as a fraction.

Any person who has spent enough time in math should be familiar with the fact that the thirds (aka 1/3, 2/3) are repeating decimals, but are rational numbers as they can be written as whole number fractions.

If you didn't know this, don't worry. You'll get it soon enough.

Hope this helped!

Murrr4er [49]3 years ago

4 0

Because it can be written as a fraction 1/3

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What are these as equalivalent equations

tatiyna

Answer:

6x - 2(x - 3) and x + 3(x - 2) - 6

The two expresaions that are quivalent are 6x - 2(x - 3) and x + 3(x - 2) - 6.

Step-by-step explanation:

First expression which is 4(x - 3) is an example of a binomial that when multiplied together, the product would be 4x - 12. Therefore, second and third expressions are the answer.

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4 0

2 years ago

The probability mass function of X is f(x)= 1/6, x 1.2...,6 then find out the value

Mumz [18]

For the given probability mass function of X, the mean is 3.5 and the standard deviation is 1.708.

A discrete random variable X's probability mass function (PMF) is a function over its sample space that estimates the likelihood that X will have a given value. f(x)=P[X=x].
The total of all potential values for a random variable X, weighted by their relative probabilities, is known as the mean (or expected value E[X]) of that variable.
Mean(μ) = 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6).
Mean(μ) = (1+2+3+4+5+6)/6
Mean(μ) = 21/6
Mean(μ) = 3.5
The square root of the variance of a random variable, sample, statistical population, data collection, or probability distribution represents its standard deviation. It is denoted by 'σ'.
A random variable's variance (or Var[X]) is a measurement of the range of potential values. It is, by definition, the squared expectation of the distance between X and μ. It is denoted by 'σ²'.
σ² = E[X²]−μ²
σ² = [1²(1/6) + 2²(1/6) + 3²(1/6) + 4²(1/6) + 5²(1/6) + 6²(1/6)] - (3.5)²
σ² = [(1² + 2²+ 3² + 4²+ 5²+ 6²)/6] - (3.5)²
σ² = [(1 + 4 + 9 + 16 + 25 + 36)/6] - (3.5)²
σ² = (91/6) - (3.5)²
σ² = 15.167-12.25
σ² = 2.917
σ = √2.917
Standard deviation (σ) = 1.708