Final answer:
Rounding 2,709,450 to the nearest ten-thousand place results in 2,710,000. The number '9' after the '4' in ten-thousand place indicates the need to round up. Scientific notation clearly communicates significant figures.
Step-by-step explanation:
Rounding to the Nearest Significant Figure
To round the number 2,709,450 to the nearest digit at the '4' place, we should first understand which '4' is being referenced in the question. Assuming we're referring to the fourth place from the left, that would be the ten-thousand place. To correctly round to this position, we look at the digit immediately to the right of the ten-thousand place, which in this case is '9'. If this digit is 5 or greater, we round up. Since '9' is greater than '5', we round up the '4' in ten-thousand place to '5'. Therefore, 2,709,450 rounded to the nearest ten-thousand digit would be 2,710,000.
Rounding to the nearest significant figure is a fundamental concept in mathematics that ensures precision based on the given conditions. When using a calculator, you might encounter a situation where the answer must be limited due to certain figures being more significant than others. For example, if a calculator gives the answer 2,085.5688, but only five significant figures are important, you would round the number to 2,085.6.
In scientific notation, all significant figures are listed explicitly. This helps to avoid any ambiguity when representing or communicating numbers. It is especially useful in calculations within fields such as Chemistry and Physics where precise measurement is crucial. Remember that different calculators may require different methods to input numbers in scientific notation, so always consult the manual or instructor if needed.