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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
mathsWhole NumbersIntroduction to Whole Numbers

### Approximation and Estimation

This page introduces approximation of a number to a given degree of approximation. The same is also referred as estimation for measurement of an object.

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The word "accurate" means: correct in details; exact.

familiarize with the terminology
accurate

The word "approximate" means: close to the actual; very near in value.

familiarize with the terminology
approximate

The accurate length of the pencil in the figure is 73mm.

Let us consider a scale that does not have graduated marks for millimeters. Using the scale, the accurate length cannot be measured. The approximate length of the pencil in the figure is 7 centimeter. Note that the value 7 is closer to the accurate length.

The accurate length of the pencil in the figure is 78mm.

Considering the scale with only centimeter marks, the approximate length of the pencil is measured as 8 centimeter. Note that the value 8 is closer to the accurate length.

In many applications, the value of measurement or count need not be accurate. It can be approximated to the nearest value to some degree.

The degree of approximation is explained as follows

•  3842 approximated to nearest 10 is 3840. The degree of approximation is to the nearest 10.

•  3842 approximated to nearest 100 is 3800. The degree of approximation is to the nearest 100.

•  3842 approximated to nearest 1000 is 4000. The degree of approximation is to the nearest 1000.

The word "degree" means amount or level to which something is present. Degree of approximation is the level to which something is approximated.

The word "estimation" means: approximation and rough calculation to the nearest value. The estimation of a count or measure is the approximate value of the count or measure.

familiarize with the terminology
estimation

Solved Exercise Problem:

What is the approximate value of 3428 to the nearest 100?

• 3400
• 3400
• 34
• 3500
• 400

The answer is "3400"

Approximation of numbers : A number may be approximated or rounded to the nearest 10, or 100, or 1000, etc. If the number is halfway or above, then it is approximated to the higher value. If not, then it is approximated to the lower value.

Solved Exercise Problem:

Estimate the value of 428 to the nearest 10?

• 420
• 42
• 430
• 430
• 30

The answer is "430"

Solved Exercise Problem:

What is the approximate value of 3450 to the nearest 100?

• 3400
• 3500
• 3500
• cannot be approximated

The answer is "3500"

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