Final answer:
Solving for x and rounding requires considering the value's significant figures and rounding the final answer according to the least precise measurement, ensuring the correct amount of significant figures is maintained.
Step-by-step explanation:
To solve for x and round to the nearest hundredth, you must look at the digit in the thousandth place to decide whether to round up. When adding, subtracting, or performing any other operations, it is essential to consider the number of significant figures in the given values and to round the final answer according to the least precise measurement. Here are examples demonstrating proper rounding:
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- Adding 56.0 (3 significant figures) and 3.44 (3 significant figures) equals 59.44, which doesn't need rounding as the answer already has three significant figures.
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- 0.00665 (4 significant figures) plus 1.004 (4 significant figures) gives 1.01065, but since we are adding a number with only four significant figures, we round the answer to 1.0107.
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- For subtraction, 45.99 (4 significant figures) minus 32.8 (3 significant figures) yields 13.19. You would round the final answer to two significant figures because 32.8 has the least number of significant figures, so the final answer is 13.
It's important always to carry extra figures through calculations and round only at the end to ensure accuracy.