Question

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please answer this,
The last digit in the finite decimal representation of the number (1/5)^2004​

Answer 1

Answer:

The decimal numeral system (also called the base-ten positional numeral system, and occasionally called denary /ˈdiːnəri/[1] or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system.[2] The way of denoting numbers in the decimal system is often referred to as decimal notation.[3]

A decimal numeral (also often just decimal or, less correctly, decimal number), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in 25.9703 or 3,1415).[4][5] Decimal may also refer specifically to the digits after the decimal separator, such as in "3.14 is the approximation of π to two decimals". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value.

The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form a/10n, where a is an integer, and n is a non-negative integer.

The decimal system has been extended to infinite decimals for representing any real number, by using an infinite sequence of digits after the decimal separator (see decimal representation). In this context, the decimal numerals with a finite number of non-zero digits after the decimal separator are sometimes called terminating decimals. A repeating decimal is an infinite decimal that, after some place, repeats indefinitely the same sequence of digits (e.g., 5.123144144144144... = 5.123144).[6] An infinite decimal represents a rational number, the quotient of two integers, if and only if it is a repeating decimal or has a finite number of non-zero digits.

Answer 2

Answer:

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The last digit of 2004 is 4.

So, if we square the number the last digit will be 6 (as 4*4 is 16)

If you further multiply the number the last digit will be 4 (as 6*4 is 24)

Again for the next power the last digit will be 6 (4*4 is 16) and so on…

So we can conclude that for even numbered power of 2004 the last digit will be 6 and for odd numbered power the last digit will be 4.

So last digit for (2004)^2n = 6 (Where n= 1,2,3….)

last digit for (2004)^2n+1 = 4 (Where n= 0,1,2,3….)