Convert the following (i) (562.13)7 = (?)10 (ii) (467.342)8 = (?)10
Question
Convert the following (i) (562.13)7 = (?)10 (ii) (467.342)8 = (?)10
Solution
(i) To convert (562.13)7 to base 10, we separate the integer part and the fractional part and convert them separately.
For the integer part 562:
57^2 + 67^1 + 2*7^0 = 245 + 42 + 2 = 289
For the fractional part .13:
17^-1 + 37^-2 = 0.14285714285714285 + 0.027210884353741496 = 0.17006802721088435
So, (562.13)7 = (289.17006802721088435)10
(ii) To convert (467.342)8 to base 10, we again separate the integer part and the fractional part and convert them separately.
For the integer part 467:
48^2 + 68^1 + 7*8^0 = 256 + 48 + 7 = 311
For the fractional part .342:
38^-1 + 48^-2 + 2*8^-3 = 0.375 + 0.0625 + 0.03125 = 0.46875
So, (467.342)8 = (311.46875)10
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The question seems to be a bit unclear, but I'll try to interpret it as best as I can. Step 1: Solve the operation inside the parentheses first, which is (137 - 58). The result is 79. Step 2: Multiply the result by 2334. The result is 184386. Step 3: Divide 157 by 47. The result is approximately 3.34 (rounded to two decimal places). Step 4: Multiply the result from step 3 by 2 raised to the power of 13. The result is approximately 27341.12 (rounded to two decimal places). Step 5: Add the results from step 2 and step 4. The result is 211727.12. Step 6: Multiply the result by -2. The final result is -423454.24. ####
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