Estimation

According to a census average of 2.76 million people use the Delhi Metro every day. Do you think this is an actual number? Did the authorities count every passenger and calculate such an average? Of course not. This is a matter of estimation of numbers. Let us learn about estimation and rounding off.

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Estimation

Often in real life situations, knowing the exact number of things is not as important. An estimate is far more practical and easier to calculate. For example, the Prime Minister of India does not need to know the exact number of students pursuing higher education in India. He only requires an estimate so he can form policies accordingly.

To find an estimate is easier, cheaper and less time-consuming than an actual count in many cases. If the situation does not warrant an exact count, an estimation is a way to go. Let us learn a few methods related to estimation.

Rounding off to nearest Tens

Let us take an example of three numbers – 14, 15 and 16. We are to round off these numbers to the nearest tens place. Now imagine these numbers on a number scale. Is 14 closer to 10 or to 20. It is closer to 10, so we can round off 14 as 10. Similarly, 16 is closer to 20, and hence we can round off 16 as 20. 15 is equidistance from both 10 and 20. It is the general practice to round up, which means 15 will be rounded off to 20 as well.

In conclusion, the numbers ending in 1, 2, 3, and 4 are rounded down, while those ending in 5, 6, 7, 8 and 9 are rounded up to the nearest tens place. For example, 47 will be rounded off to 50, but 83 will be rounded off to 80.

Rounding off to Hundreds

The same principle applies here. We see if the number is closer to the lower hundred or the higher one on the number line. We will better understand with examples.

Rounding off the numbers 416 and 485. Here 416 is definitely closer to 400, so we round it off to 400. And 485 will be rounded off to the next hundred, which is 500. One point to be noted, 450 while right in between 400 and 500 is generally rounded up to 500.

Example; Round off 43 to the nearest hundred. Here 43 is closer to 0 than to 100, and so we will round it off as 0.

Rounding off to Thousands

All numbers from 0 to 499 being closer to 0 on the number line will be rounded off as 0. Numbers from 500 to 999 will be rounded off as 1000. And the same principle will apply to all the larger numbers as well. The numbers closer to the lower thousand will be rounded down, and from 500 onwards will be rounded up.

Example: Round off the following numbers
1234 → 1000
7399 → 7000
9845 → 10000
3500 → 4000

Estimating Sums and Differences

Sometimes we don’t just estimate numbers, we all estimate certain mathematical productions. It makes calculating easier while giving us an estimation of the answer we require. For example, you and your friends went on a donation drive. You each collected 435, 664,  410 and 239 rupees. So if you wanted to add up the amounts, an estimation of the sum would be efficient.

We will begin by rounding off the numbers to the nearest tens and then adding up the estimated numbers

• Estimated Sum = 440 + 660 + 410 + 240 = 1750
• Actual Sum = 435 + 664+ 410 + 239 = 1748

As you can see from the calculations above the sums are very close to each other. The estimation of the sums was easier to calculate and time-saving as well. Let us now see some examples of estimation of differences and products.

Estimation of Differences/Subtraction

Estimate: 5733 – 458
If we round off to thousands, the answer will be
5733 rounds off to 6000
458 rounds off to 0
This does not seem to be an accurate answer at all.

So now we round off to hundreds
5733 rounds off to 5700
458 rounds off to 500
The difference is 5200, and this seems like an accurate and reasonable estimation.

Solved Example for You

Question 1: Round-off 4353 to nearest 100.

1. 4360
2. 4200
3. 4300
4. 4400

Answer : The correct answer is “D”. 4353 is closer to 4400 than 4300 on the number line.

Question 2: (7268−2427) estimated to the nearest hundred is

1. 4800
2. 4900
3. 4841
4. 5000

Answer : The correct option is “A”. We have (7268−2427) = 4841. Rounding off 4841 to nearest hundred we get 4800.

Question 3: Why is rounding important?

Answer: Rounding numbers is essential as it makes them simpler and easier to use. Although they are somewhat less accurate, their values are still moderately close to what they initially were. Lastly, it’s sometimes just easier to work your way rounded numbers, as exact numbers are not only needed.

Question 4: Why do you round 5 up?

Answer: We round up 5 because everyone prefers even numbers. Thus, when we round up 5, it means that as many numbers are rounded up as they are rounded down. So, if we consider single-digit numbers, then we round down 0, 1, 2, 3, 4 and round up 5, 6, 7, 8 and 9.

Question 5: What is 3.5 rounded to the nearest tenth?

Answer: To round 3.5 to the nearest tenth, we need to consider the hundredths’ value of 3.5. Thus, it is 0 and equal or more than 5. Thus, the tenths value of 3.5 will increase by 1 to 6.

Question 6: What does Rounding off to Thousands mean?

Answer: All numbers that are from 0 to 499 while being closer to 0 on the number line will be rounded off as 0. Further, we will round off numbers from 500 to 999 as 1000. Thus, we will apply the same principle to all the larger numbers as well. So, we will round down the numbers closer to the lower thousand and round up those from 500 onwards.