from the list 0, 14, 2/3 , pi, √7, -11/14, 2.34, -19,55/8, -sqrt{17}, 3.21, and -2.6, identify each of the following.

from the list 0, 14, 2/3 , pi, √7, -11/14, 2.34, -19,55/8, -sqrt{17}, 3.21, and -2.6, identify each of the following.

Question
Decimals
asked 2021-03-02
from the list \(\displaystyle{0},{14},\frac{{2}}{{3}},\pi,√{7},-\frac{{11}}{{14}},{2.34},-{19},\frac{{55}}{{8}},-\sqrt{{{17}}},{3.21},\) and -2.6, identify each of the following.

Answers (1)

2021-03-03

Step 1

Real numbers are the sum of rational numbers and irrational numbers. All the given numbers are real numbers. Rational number are the numbers that can be expressed as the form of p/q where p and q are the integers. These are terminating decimals. Terminating decimals are the decimals which have a finite number of digits after the decimal point. Therefore, \(\displaystyle{0},{14},{\frac{{{2}}}{{{3}}}},-{\frac{{{11}}}{{{14}}}},{2.34},{\frac{{{55}}}{{{8}}}},-{19},{3.21},-{2.6}\) are rational numbers since these are satisfying the definition of rational number.

Step 2

Irrational numbers is a number that cannot be expressed as the form of p/q where p and q are the integers. It cannot be expressed in the form of decimal expansions which is neither terminate nor become periodic and every transcendental number is irrational. Therefore, \(\displaystyle\pi,\sqrt{{{7}}},\sqrt{{{17}}}\) are irrational numbers since these are satisfying the definition of irrational number. Integers are the number that can be written without the fraction number. Therefore,\(\displaystyle{0},{14},-{19}\) are integers since these are satisfying the definition of integers.

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