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1.3.3: Calculator Skills Involving Decimals

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    In this lesson, you will practice using a calculator to perform operations with decimals and utilize various strategies to determine the reasonableness of your answers.

    Using Estimation to Evaluate the Reasonableness of Your Answer

    Estimation is one strategy that you can use to determine if your final answer makes sense.

    Definition: Estimation

    Estimation is the process of determining an expected value of a computation.

    Common words used in estimation are about, near, and between.

    One strategy that we can use when estimating a result is by rounding each number.

    In the rounding process, it is important to note two facts:

    1. The rounding that is done in estimation does not always follow the rules of rounding discussed in the previous lesson on rounding whole numbers and decimals. Since estima­tion is concerned with the expected value of a computation, rounding is done using convenience as the guide rather than using hard-and-fast rounding rules. For example, when estimating a division problem, it may be more convenient to divide by 20 than by 30.
    2. Since rounding may occur out of convenience, and different people have differ­ent ideas of what may be convenient, results of an estimation done by rounding may vary. For a particular computation, different people may get different estimated results. Results may vary.
    Example 1

    Use your calculator to calculate 5.7 + 11.9. Then estimate the sum to determine whether your answer is reasonable.

    Answer

    Using a calculator, we find that the sum is 17.6.

    To check that this result is reasonable, we can estimate by rounding 5.7 to 6 and 11.9 to 12. Then 6 + 12 = 18, which is close to 17.6, so the answer is reasonable.

    Example 2

    Use your calculator to calculate 5.123 + 18.47. Then estimate the sum to determine whether your answer is reasonable.

    Answer

    Using a calculator, we find that the sum is \(23.593\).

    To check that this result is reasonable, we can estimate by rounding 5.123 to 5 and 18.47 to 18. Then 5 + 18 = 23, which is close to 23.593, so the answer is reasonable

    Example 3

    Use your calculator to calculate 50 − 37.42. Then estimate the difference to determine whether your answer is reasonable.

    Answer

    Using a calculator, we find that the difference is \(12.58\).

    To check that this result is reasonable, we can estimate by rounding 37.42 to 40 instead of 38, since 50 − 40 is easier to mentally calculate than 50 − 38. Then 50 − 40 = 10, which is close to 12.58, so the answer is reasonable.

    Example 4

    Use your calculator to calculate 4.77 − 6.3. Then estimate the difference to determine whether your answer is reasonable.

    Answer

    Using a calculator, we find that the difference is \(-1.53\).

    To check that this result is reasonable, we can estimate by rounding 4.77 to 5 and 6.3 to 6. Then 5 − 6 = -1, which is close to -1.53, so the answer is reasonable.

    Example 5

    Use your calculator to calculate 4.5(6.107). Then estimate the product to determine whether your answer is reasonable.

    Answer

    Using a calculator, we find that the product is \(27.4815\).

    To check that this result is reasonable, we can estimate by rounding 4.5 to 5 and 6.107 to 6. Then 5(6) = 30, which is close to 27.4815, so the answer is reasonable.

    Using Number Sense to Evaluate the Reasonableness of Your Answer

    In the previous examples, we used estimation to evaluate the reasonableness of our answers because we were:

    • adding or subtracting numbers
    • multiplying numbers
    • working with values that were easy to round

    In these cases, we could round the numbers to simpler values and perform the calculation mentally.

    But, using estimation is not always practical. Sometimes it is better to rely on number sense when we are:

    • dividing with decimals
    • working with multi-step expressions
    • estimating would be difficult or confusing

    In these cases, think about the size of the numbers and how the operation affects the result. For example:

    • Dividing by a number greater than 1 makes the result smaller.
    • Dividing by a number less than 1 makes the result larger.

    If your answer fits what you expect, it is likely reasonable.

    Example 6

    Use your calculator to calculate 0.04 × 0.087. Then use estimation or number sense to determine if the answer is reasonable.

    Answer

    Using a calculator, we find that the product is \(0.00348\).

    Since both numbers are less than 1, the product must be very small. Multiplying the leading digits gives 4 × 9 = 36, so the result should be around 0.003 to 0.004. Because 0.00348 is in this range, the answer is reasonable.

    Example 7

    Use your calculator to calculate 0.28 ÷ 4. Then use estimation or number sense to determine if the answer is reasonable.

    Answer

    Using a calculator, we find that the quotient is \(0.07\).

    Since 0.28 is less than 1, dividing by 4 should give a smaller number. Since 28 ÷ 4 = 7, the result 0.07 makes sense.

    Example 8

    Use your calculator to calculate −23.492 ÷ (−0.04). Then use estimation or number sense to determine if the answer is reasonable.

    Answer

    Using a calculator, we find that the quotient is \(587.3\).

    To check that this result is reasonable, note that a negative divided by a negative gives a positive result. Also, dividing by a number less than 1 makes the result larger. Since 587.3 is much larger than 23.492, the answer is reasonable.

    For more complex expressions, focus on entering the expression carefully and checking that your answer makes sense based on the size of the numbers.

    Exercise 9

    Use your calculator to calculate 30(0.4) + (0.5)2.

    Answer

    Using a calculator, we find that the quotient is \(12.25\).

    Exercise 10

    Use your calculator to calculate 1.8(22.4 + 2.6).

    Answer

    Using a calculator, we find that the quotient is \(45\).

    Exercise 11

    Use your calculator to calculate 16 ÷ (0.6 + 0.4).

    Answer

    Using a calculator, we find that the quotient is \(16\).

    Exercise 12

    Use your calculator to calculate (3.2 + 0.8)(0.9 − 0.3).

    Answer

    Using a calculator, we find that the quotient is \(2.4\).

    This page titled 1.3.3: Calculator Skills Involving Decimals was last modified on Wed, 13 May 2026 20:55:51 GMT and is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Denny Burzynski and Wade Ellis, Jr. (OpenStax CNX) via source content that was edited to the style and standards of the LibreTexts platform.