C1.09: Exercises

In the examples 7-12 above, the same answer was given with several different forms of notation. You do not have to write all of those different ways for every answer, unless you are explicitly asked to give several different forms of the answer.   You must understand how to write all the forms, of course.

Part I.

  1. Round to the nearest hundredth. (a) 3.14738     (b)       0.73372         (c) 0.0032
  2. Round to the nearest ten. (a) 817         (b) –1123     (c) 74.567
  3. Round 64.7 to the nearest ten.
    1. Do it in one step, correctly.
    2. Illustrate the error that occurs if you try to do it in two steps – first rounding to the nearest one and then rounding that result to the nearest ten.
  4. For each of the following numbers, fill in the blanks in the table.
    Number Implied precision in words Implied precision in numbers Significant digits underlined
    17.3
    18
    18.0
    100.6
    83.20
    97.1080
    13000
    20800
  5. Draw a number line that includes the values from 0 to 3.       On that number line, label the points corresponding to the three numbers 0.1, 1.56, and 2.478.
  6. Draw a number line that includes the values from 2.0 to 3.0 and label the points corresponding to these numbers: 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, and 3.0.
  7. Draw a number line that includes the values from 2.2 to 2.4, and label 2.2, 2.3, and 2.4. Then find the cut-off values for the numbers that would round to 2.3.
  8. Consider numbers rounded to the nearest hundredth.
    1. Write several numbers between 7.6000 and 7.6500 and round each of them to the nearest hundredth.
    2. Draw a number line and use it to illustrate which numbers are to be rounded to 7.63.
    3. Suppose we report a number as 7.63, rounded to the nearest hundredth. Write an interval that gives the actual values that are consistent with a rounded value of 7.63
  9. If a measured number is reported as 63 feet, rounded to the nearest foot, what interval of possible actual values are consistent with that?
  10. A measured number is reported as 0.03724 kilometers
    1. state the implied precision as a number
    2. state the implied precision in words
    3. underline the significant digits
    4. find the interval of possible actual values consistent with this number.
  11. A measured number is reported as 1.27 liters
    1. state the implied precision as a number
    2. state the implied precision in words
    3. underline the significant digits
    4. find the interval of possible actual values consistent with this number and what are several ways this might be reported?
  12. Pay careful attention to when trailing zeros are conveying precision.
    1. If a measured number is reported as 52700 feet, rounded to the nearest hundred feet, underline the significant digits and find the interval of possible actual values that are consistent with that.
    2. If a measured number is reported as 0.30 meters, rounded to the nearest hundredth of a meter, underline the significant digits and find the interval of possible actual values that are consistent with that.
  13. If a measured number is reported as 12 meters,
    1. what is the interval of actual values consistent with that,
    2. what is the maximum amount that the actual value could differ from the reported value
    3. what is the maximum amount of error as a percentage of the reported number?
  14. If a measured number is reported as 12.0 meters,
    1. what is the interval of actual values consistent with that,
    2. what is the maximum amount that the actual value could differ from the reported value
    3. what is the maximum amount of error as a percentage of the reported number?

Part II.

  1. Consider 12.1464.
    1. Round 12.1464 to the nearest hundredth.
    2. Round 12.1464 to the nearest tenth.
    3. Round 12.1464 to the nearest hundredth and then round that result to the nearest tenth. Is this a good method of getting a rounded number for 12.1464 to the nearest tenth? Explain.
  2. Consider 8.5478
    1. Round 8.5478 to the nearest hundredth.
    2. Round 8.5478 to the nearest tenth.
    3. Round 8.5478 to the nearest hundredth and then round that result to the nearest tenth. Is this a good method of getting a rounded number for 8.5478 to the nearest tenth? Explain.

For each of the given numbers in problems 17-24,

  1. state the implied rounding precision as a number
  2. state the implied rounding precision in words
  3. underline the significant digits
  4. find the interval of possible actual values consistent with this rounded number.
  5. what is the maximum amount that the actual value could differ from the reported value?
  6. what is the maximum amount of error as a percentage of the reported number?
  1. The rounded number 0.71
  2. The rounded number 8.93
  3. The measured number $54,000
  4. The measured number $157,000
  5. The measured number 2.347 liters
  6. The measured number 18.978
  7. The measured number 0.0072
  8. The measured number 0.0378

For each of the given numbers in problems 25-28,

  1. underline the significant digits
  2. find the interval of possible actual values consistent with this rounded number.
  1. The measured number 0.00406
  2. The measured number 0.0003802
  3. The measured number 12.000406
  4. The measured number 9.0382
  5. Consider these three rounded numbers
    1. For the measured number 7 meters, underline the significant digits and find the interval of actual values.
    2. For the measured number 7.0 meters, underline the significant digits and find the interval of actual values.
    3. For the measured number 7.00 meters, underline the significant digits and find the interval of actual values.
    4. Do these three reported rounded numbers convey identical information?
  6. Consider these three rounded numbers.
    1. For the measured number 82 meters, underline the significant digits and find the interval of actual values.
    2. For the measured number 82.0 meters, underline the significant digits and find the interval of actual values.
    3. For the measured number 82.00 meters, underline the significant digits and find the interval of actual values.
    4. Do these three reported rounded numbers convey identical information?