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Ch.1 - Matter, Measurement & Problem Solving
Chapter 1, Problem 113

Do each calculation without your calculator and give the answers to the correct number of significant figures: a. 1.76 * 10^3 > 8.0 * 10^2 b. 1.87 * 10^-2 + 2 * 10^-4 - 3.0 * 10^-3 c. [(1.36 * 10^5)(0.000322) > 0.082](129.2)

Verified step by step guidance
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Step 1: For part (a), identify the number of significant figures in each number. 1.76 * 10^3 has three significant figures, and 8.0 * 10^2 has two significant figures.
Step 2: Perform the division in part (a) without a calculator. Divide the coefficients (1.76 by 8.0) and subtract the exponents of 10 (3 - 2).
Step 3: For part (b), align the numbers by their exponents. Convert 1.87 * 10^-2, 2 * 10^-4, and 3.0 * 10^-3 to the same power of ten if necessary.
Step 4: Add and subtract the coefficients in part (b) while keeping track of the significant figures. The result should have the same number of decimal places as the number with the least decimal places.
Step 5: For part (c), first perform the multiplication inside the brackets. Multiply 1.36 * 10^5 by 0.000322, then divide by 0.082. Finally, multiply the result by 129.2, ensuring the final answer has the correct number of significant figures.
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