MathsKnowing Our NumbersKnowing our Numbers – Estimating Outcomes – Part 3

Knowing our Numbers – Estimating Outcomes – Part 3

Table of Contents

  • Estimating a Sum
  • Estimating a Difference
  • Estimating a Product
  • Summary
  • What’s Next?

In our previous segment, we looked at some examples to understand how estimation depends on situations. Estimating by rounding off numbers to nearest 10, 100 and 1000, give us different values, and all are correct estimations depending on the situation.

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    In this segment, we will now solve some problems on estimating a sum, difference and a product.

    How to estimate a sum?

    To estimate a sum, we first need to round up the given numbers to their nearest 10, 100 or 1000 (depending on the question or situation). We can then add the rounded-off values normally.

    Example 1: Estimate 15,367 + 7,298 to the nearest thousand

    Step 1: Rounding off to nearest 1000

    15367 ~ 15000 (∵ 15367 is closer to 15000 than 16000)

    7298 ~ 7000 (∵ 7298 is closer to 7000 than 8000)

    Step 2: Addition

    15000 + 7000 = 22,000

    The estimated sum of 15367 and 7298 is 22,000.

    Example 2: Estimate 290 + 3,725

    In this question, we are not given any instructions of rounding off the numbers. In such a case, we will apply the following logic:

    Rounding off the values to the nearest 1000 will round off 290 to 0. This will make our estimations less accurate.

    So, we can either round off the values to the nearest 10 or nearest 100. While rounding off to the nearest 10 may give us a much more accurate estimate, it will be more time consuming as compared to rounding off the values to nearest 100

    Hence rounding off to 100 is the preferred method here.

    Step 1: Rounding off to nearest 100

    290 ~ 300 (∵ 300 is closer to 290 than 200)

    3725 ~ 3700 (∵ 3700 is closer to 3725 than 3800)

    Step 2: Addition

    3700 + 300 = 4000

    The estimated sum of 290 and 3725 is 4,000.

    How to estimate a difference?

    For estimating differences, we follow the same procedure as we did for addition – first round up the given numbers to their nearest 10, 100 or 1000 (depending on the question or situation) and then proceed to subtract the rounded-off values normally.

    Let us see an example –

    Example: Estimate 83,298 – 3,059

    Rounding off to a nearest 10 will make it time consuming.

    We can round it off the given numbers to either nearest 100 or 1000.

    Rounding off to nearest 1000

    Step 1:

    83298 ~ 83000

    3059 ~ 3000

    Step 2: Subtraction

    83000 – 3000 = 80000

    The estimated difference between 83,298 and 3,059 is 80,000.

    Rounding off to nearest 100

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