Decimal Expansion Of Real Numbers Finding Decimal Expansion

Decimal Expansion Of Real Numbers Finding Decimal Expansion Go through the following examples to understand the concept of real numbers and their decimal expansion. example 1: prove that 3.1426 is a rational number. solution: to prove: 3.1426 is a rational number. the number 3.1426 can be written as 31426 10000. 31426 10000 = 3.1426. Ans: given rational number is 13 3125. also, given that they have terminating decimal expansion. write the prime factors of the denominator 3125 of the given number. ⇒ 13 3125 = 13 5 × 5 × 5 × 5 × 5 = 13 5 5. multiply and divide both sides of the number by 2 5. ⇒ 13 5 5 × 2 5 2 5 = 13 × 2 5 10 5.

Decimal Expansion Of Real Numbers Finding Decimal Expansion #introductiontouniversitymaths #decimalexpansiondecimal expansion is a way to express a real number. we introduce an important characterization of rational n. Decimal expansion. we can expand a whole number like this: 563 = 5×100 6×10 3×1. so 563 is a sum of each digit multiplied by its place value (hundreds, tens, units). we can also do this with a decimal number such as 37.29: 37.29 = 3×10 7×1 2× 1 10 9× 1 100. here is how it looks after the multiplications:. Example: the real number \[\dfrac{4}{9}\] decimal expansion is \[0.444444 \ldots \] after the decimal point, the number $4$ is repeated. such numbers are the non terminating numbers represented in decimal expansion. decimal expansion of irrational numbers. irrational numbers are those that cannot be expressed in the form of $\dfrac{a}{b}$. As a sequence, the decimal expansion isn't equal to one; we can say that it represents one, but there is a slight difference between a sequence representing a number and it being equal to it. for " .999 = 1" to be seen as true, it must be interpreted as "the sequence of symbols decimal point nine nine nine ellipsis represents the number one.