Q1, if 3245 to base six is=xnine find x

Chemistry

ScanSolve AI Answer

Answer

1022

Step-by-step solution

3 steps

The problem "if 3245 to base six is=xnine find x" is interpreted as converting the number 324563245_6 to base 9, where xx represents the digits of the number in base 9.

  1. Convert 324563245_6 to base 10.

    To convert a number from any base to base 10, multiply each digit by the base raised to the power of its position, starting from 0 for the rightmost digit before the decimal point.

    32456=3×63+2×62+4×61+5×603245_6 = 3 \times 6^3 + 2 \times 6^2 + 4 \times 6^1 + 5 \times 6^0 32456=3×216+2×36+4×6+5×13245_6 = 3 \times 216 + 2 \times 36 + 4 \times 6 + 5 \times 1 32456=648+72+24+53245_6 = 648 + 72 + 24 + 5 32456=749103245_6 = 749_{10}
  2. Convert 74910749_{10} to base 9.

    To convert a number from base 10 to another base, repeatedly divide the base 10 number by the new base and record the remainders. The new number is formed by reading the remainders from bottom to top.

    749÷9=83 remainder 2749 \div 9 = 83 \text{ remainder } 2 83÷9=9 remainder 283 \div 9 = 9 \text{ remainder } 2 9÷9=1 remainder 09 \div 9 = 1 \text{ remainder } 0 1÷9=0 remainder 11 \div 9 = 0 \text{ remainder } 1

    Reading the remainders from bottom to top, we get 102291022_9.

  3. Identify xx.

    Since 32456=x93245_6 = x_9, and we found 32456=102293245_6 = 1022_9, then xx is 1022.

    x=1022x = 1022

    The value of xx is 1022\boxed{1022}.

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