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What number doesnt not appear in the first 30 places of pi's decimal expansion?
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∙ 12y ago
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∙ 12y ago
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decimal expansion of irrational number is non terminating and?
The decimal expansion of an irrational number is non terminating and non recurring
What is the decimal expansion of an irrational no. is?
It is the decimal approximation to the value of the irrational number.
What can you say about the decimal expansion of any rational number?
If its a rational number then its decimal equivalent can be expressed as a fraction
Is a number with an unending decimal expansion irrational?
No. If the decimal expansion falls into a repeating pattern (however long) then the number is rational. For example, 0.33... is the rational number 1/3. or 0.04142857142857... where the pattern 142857 continues forever is the rational number 29/700.
What is the decimal expansion of the number 357?
It is 300 + 50 + 7.
What is the decimal expansion of an irrational number?
A decimal expansion means to write out the base 10 digits of a number. Because irrational numbers do not have a closed form, the decimal expansion will always be an approximation. Consider the irrational number pi, which has the following decimal expansion: 3.14159265... Of course there are more digits to pi than that, which is denoted by the "...". It is sadly impossible to list ALL of the digits of an irrational numbers, since if there were a finite number of digits, you could express it as a fraction, which would not be irrational.
Does the number 30 have a decimal expansion?
Its decimal "expansion" is 30, as in the question. You could express it as 30.000... except that doing so would imply a greater degree of precision.
Can you make this amount of money 168.9.210.12.?
No. This number is an impossible decimal. Only one decimal can appear in a number at a time.
Is the decimal expansion of an irrational number is finite?
No. It must be infinite AND non-recurring.
What is the difference between the decimal expansion in irrational and rational numbers?
Decimals that terminate or repeat in some fashion are rational, while decimals that expand forever are irrational.
What are the two possibilities for the decimal expansion of a rational number?
It terminates or has a infinite repeating expression.
Why does irrational numbers don't stop?
Because if they stopped they could be expressed as a ratio. Suppose the decimal expansion of an irrational stopped after x digit AFTER the decimal point. Now consider the number n, which is the original number, left and right of the decimal, but without the decimal point. This is the nummerator of your ratio. The denominator is 1 followed by x zeros. It is easy to show that this ratio repesents the decimal expansion of the number
