Some times while solving mathematical expressions, we do not need to find out an exact value but an approximate value is sufficient. We have already seen in the previous article about simplification where we solved the complex expressions into much simpler form. Approximation or estimation is another technique of solving mathematical expressions. It is a rough answer to the question. In approximation we do not require to find the exact value of the expression but an approximate value through near rounding off is enough. The symbol for approximately equal to is ≅.
One very simple form of approximation is rounding off. Rounding is the significant talent you must learn to rapidly guess an answer for mathematical question. This is where you make a long number simpler. By rounding off we try to express the numbers in terms of the nearest unit, ten, hundred, tenth, or a certain number of decimal places. Rounding off a number means making a number simpler but, at the same time keeping its value closest to that number. It is important to note that, rounding off method will not affect the final value of the mathematical expression.
We ROUND UP the numbers which are equal to or greater than 5. We ROUND DOWN the numbers which are less than 5. For instance, rounding off a number to nearest hundred means, finding the multiple of 100 which is closest to the original number; similarly, rounding off to nearest tenth means finding the multiple of 1/10 which is closest to the original number.
For example, consider approximation of 1,676
Replace the digit at unit’s place by 0. If the replaced digit is 5 or more, then add 1 to the digit at tens place, otherwise digit at tens place remains unchanged.
For example,
Replace the digit at units and tens place by 00. If the replaced digit at tens place is 5 or more, then add 1 to the digit at hundreds place, otherwise digit at hundreds place remains unchanged.
For example,
Replace the digit at units, tens and hundreds place by 000. If the replaced digit at hundreds place is 5 or more, then add 1 to the digit at thousands place, otherwise digit at hundreds place remains unchanged.
For example,
If the digit immediately to the right of nth place is 5 or more, then add 1 to the digit at nth place, otherwise the digit at nth place remains unchanged. Finally delete all the numbers to the right of nth place.
For example,
Other Interesting estimations in daily life
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Estimated Time of Arrival (ETA) This term is often used when travelling in trains, buses, planes, ships etc. The ETA is depends on distance and speed of travel. We say it as estimated because we do not consider the unforeseen changes occurring during the journey. For example, the flight may arrive early or arrive late depending on weather conditions similarly road journey may take longer than expected due to traffic jams etc. |
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Estimation of Work While starting to build a house or getting a plumber work done or in all similar conditions we generally calculate work estimates. While calculating work estimates, we analyze the time frame within which the work would be completed and then multiply it by their hourly wages, extra work hours and so on. This is actually done not to get surprised by unexpected bill. |
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