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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.
mathsDecimalsFundamentals of Decimals

### Decimals in Number-Line

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In whole numbers, we learned that the ordinal-property of the numbers is defined by 0<1<2<3< cdots.

In integers, we learned that the ordinal-property of the numbers is extended to cdots <-3<-2<-1<0<1<2<3< cdots.

In fractions, we learned that the fractions are placed with in the integer numbers and maintains the ordinal property.

Do decimals have ordinal property?

• ordinal property for decimals is same as that of fractions
• ordinal property for decimals is same as that of fractions
• ordinal property is not applicable for decimals

The answer is "ordinal property for decimals is same as that of fractions".

The ordinal property is best captured by the number-line.

•  Number-line of whole numbers starts from 0 and extends in one direction. It consists of points at positions 0,1,2, cdots.

•  Number-line of integers extends in both the directions. It consists of points at positions cdots, -2,-1,0,1,2, cdots

•  Number-line of fractions is same as that of integers, and fractions are placed on points on the line segments between the integers. Which of the following describe the number-line of decimals?

• the number-line of decimals is the points at positions cdots, -2,-1,0,1,2, cdots
• the number-line of decimals is same as that of fractions as decimals are an alternate representation of fractions
• the number-line of decimals is same as that of fractions as decimals are an alternate representation of fractions

The answer is "the number-line of decimals is same as that of fractions as decimals are an alternate representation of fractions".

Consider the number line of decimals. Where is the decimal 0.5 located in the number-line?

• 0.5 is not located in number-line
• 0.5 is between integers 0 and 1
• 0.5 is between integers 0 and 1

The answer is "0.5 is between integers 0 and 1". The line-segment between 0 and 1 is split into 10 equal pieces. 0.5 is at the position of 5th piece as shown in the figure.

Consider the number line of decimals.

Where is the decimal 2.34 located in the number-line?

• 2.34 is not located in number-line
• 2.34 is between integers 2 and 3 at 34th position of 100 pieces
• 2.34 is between integers 2 and 3 at 34th position of 100 pieces

The answer is "2.34 is between integers 2 and 3 at 34th position of 100 pieces". The line-segment between 2 and 3 is split into 100 equal pieces. 2.34 is at the position of 34th piece.

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