? asked in Science & MathematicsMathematics · 1 decade ago

Math problem help.?

What is the Ones digit of 13 raised to 2003 ?

2 Answers

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  • MsMath
    Lv 7
    1 decade ago
    Favorite Answer

    Let's look at some powers of 13.

    13^0 = 1

    13^1 = 13

    13^2 = 169

    13^3 = 2197

    13^4 = 28561

    13^5 = 371,293

    13^6 = 4,826,809

    13^7 = 62,748,517

    Look at the ones digits in the above numbers, do you see the pattern?

    1, 3, 9, 7, 1, 3, 9, 7, and so on.

    Divide 2003 by 4

    2003/4 = 500 remainder 3.

    So the ones digit will be a 7

  • 1 decade ago

    7

    --------

    Reason:

    Since 3^4 = 81, the last digit of 3^4 is 1.

    The last digit of 13^4

    = the last digit of 3^2003

    = the last digit of 3^2000(3^3)

    = the last digit of (3^4)^500(3^3)

    = the last digit of (3^3)

    = 7

  • 1 decade ago

    4.719 x 10^955

    Overflows most calculators. However,

    2003 * Log(3) = 955.67387

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