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notebook lessons for math
Teaching with Smartboard Episode 27 Balloons
Greatest Possible Error
Introduction
No measurement is exact. Every time we make a measurement a certain degree of error creeps in, however careful we are.
Measurement errors depend on the measuring instrument used and how we use the instrument. The graduations on a measuring instrument make it possible to get more precise measurements. The greater the number of graduations on the instrument, the more precise the measurement.
For example,
Brian and Amy measured the length of the same notebook with two different rulers. Brian measured the length of the notebook to be 21.5 cm and Amy’s measurement was 21.46 cm. Choose the more precise measurement.
Brian’s measurement 21.5 cm implies that the measurement was carried out to the nearest tenth of a centimeter.
Amy’s measurement 21.46 cm implies that the measurement was carried out to the nearest hundredth of a centimeter.
Smaller measurements are more precise.
So 21.46 cm would be a better approximation of the two.
Let’s look at one more example.
An object was weighed using two different scales, Scale-1 and Scale-2.
Scale-1 had marking in kg.
Scale-2 was graduated. It had 10 divisions between any two whole numbers on the scale which means each small graduation is equal to 0.1 kg.
The weight of the object on Scale-1 was 67 kg. The measurement of the same weight on Scale-2 was 67.3 kg. Which scale is more precise?
Clearly, Scale-2 is more precise.
Whenever we use a graduated measuring instrument, we must first determine the unit that the instrument is using, and then we must find out the smallest unit on the instrument.
By definition,
“The Greatest Possible Error in a measurement is half the smallest unit used. “
Some examples on “Greatest Possible Error” should help make things clearer.
Example 1
Suppose your friend says that the height of her study table is ABOUT 28 inches. Find the greatest possible error of the measurement.
Solution:
We have no clue how your friend measured the height.
Let’s just trust your friend and go forward.
Your friend says that the height of the table is ABOUT 28 inches. So, this measure is just an ESTIMATE not the actual measure.
Nothing has been stated about how the measurement is rounded. Let’s assume your friend rounded the measurement to the nearest inch. In that case, what could be the EXACT height of the table?
If your friend’s measurement is right, then any number that would round off to 28 inches would be reasonable.
Any number between 27.5 and 28.5 feet is reasonable for the exact height. Because, any number greater than 27.5 would round up to 28 and any number less than 28.5 would round down to 28.
The exact height could be 28 inches “+ or – 0.5 inch.”
Therefore the Greatest Possible Error of the measurement is 0.5 inch.
In other words, by definition,
“The greatest possible error is one half of the smallest measuring unit used.”
The height of the table is 28 inches and this measurement is made to the nearest inch. So, the Greatest Possible Error will be half of one inch which is 0.5 inch.
Example 2
The length of a stick is stated as 5.4 cm. Find the greatest possible error of the measurement.
Solution:
“The greatest possible error is one half of the smallest measuring unit used.”
The length of a stick is stated as 5.4 cm. This measurement is made to the nearest tenth of a centimeter. So, the Greatest Possible Error will be one half of 0.1 cm which is 0.05 cm.
Example 3
The length of a window is 16 feet to the nearest foot. What is the greatest possible error of the measurement?
Solution:
“The greatest possible error is one half of the smallest measuring unit used.”
The length of a window is 16 feet and this measurement is made to the nearest foot. So, the Greatest Possible Error will be half of one foot which is 6 inches. (1 feet = 12 inches)
Example 4
A finger ring weighs 3.75 grams. Find the greatest possible error of the measurement.
Solution:
“The greatest possible error is one half of the smallest measuring unit used. “
The weight of a finger ring is 3.75 grams and this measurement is made to the nearest hundredth of a gram.
So, the greatest possible error is one half of 0.01 grams which is 0.005 grams.
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About the Author
I’m Chandrajeet, an in-house writer for iCoachMath. iCoachMath is an effective, convenient, easy-to-use online Math Program which has been used by thousands of students, teachers, and parents. iCoachMath strives to lead K-12 students to excellence in math by offering quality web-based educational solutions. iCoachMath’s instructional and lesson materials are aligned to State Curriculum Standards in all 50 states (USA).
iCoachMath
Be specific!? How do Y-O-U study ideas like Parts to Whole concepts? Terminology? Story comprehension? Math?
Most teachers do not teach kids HOW to study, they just give kids terminology (as an ex) and send them home saying,”Study for Friday’s test.” Most kids study instinctively. Others, now adults, have had to develop compensatory skills (tricks to get the job done that work for them). I was one such student. So, to the instinctive student I ask you to reflect on HOW you “study” and to the student who developed compensations, I ask what worked for you?
Previously, the best response I got was:
Read the questions 1st! Then write down every bold print title and the italicized words and their def. for the next days lessons. Then read that portion of the text. When reading for comprehension in a library book write down the characters as they show up and tell who they are in relation to the main character. Write down places,cities,year,century,etc… When you finish reading for the time period, read over your notes and put the notes with the book or put in a certain section in your notebook
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