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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.
mathsDecimalsConversion of Decimals

### Conversion of Fraction and Decimals

This page provides a simple overview of conversion between fractions and decimals.

A fraction is converted to the equivalent decimal by long division method.

A decimal is converted into its equivalent fraction by introducing the denominator based on the number of digits after decimal points.

click on the content to continue..

What are "decimal numbers"?

• multiples of primes
• standardized fractions
• standardized fractions

The answer is "decimal numbers are standardized fractions".

What is the decimal representation of 1/2?

Note: By first principles, decimals are fractions with denominator 10, 100, 1000 etc. Since the denominator is standardized, it is dropped and is represented with a decimal point.

• 0.12
• 0.5
• 0.5

The answer is "0.5".

By first principles, 1/2 is converted to the equivalent fraction 5/10, which is 0.5 in decimals.

Convert the fraction 3/8 to decimal?

• 0.375
• 0.375
• 0.125

The answer is "0.375".

This is explained in next page.

Considering converting the fraction 3/8 to decimal.

By first principles, the fraction has to be converted into an equivalent fraction having denominator one of 10, 100, 1000, etc.

8 is not a factor of 10. So the fraction cannot be converted to an equivalent fraction with denominator 10

8 is not a factor of 100 either. So the fraction cannot be converted to an equivalent fraction with denominator 100.

8 is a factor of 1000 = 8xx125. So, the denominator and numerator are multiplied by 125.

3/8 = (3xx125)/(8xx125) = 375/1000

375/1000 = 3/10 + 7/100 + 5/1000

=0.375 in decimal Noting the above, a simplified procedure is devised: By long division method, the decimal is calculated. This is shown in the figure.

Converting a Fraction to a Decimal -- simplified procedure : A fraction is converted to the equivalent decimal by long division method. An example, converting 3/8 to decimal is given in the figure.

Convert 5/4 into decimal.

• 0.125
• 1.25
• 1.25

The answer is "1.25".

By long division method,

Convert 35/2 into decimal.

• 0.175
• 17.5
• 17.5

The answer is "17.5".

By long division method,

We learned that the fractions can be converted to decimals. Similarly, decimals can be converted to fractions too.

Convert 6.75 in to the equivalent fraction

• 675/1000 = 27/40
• 6 + 75/100 = 6 3/4
• 6 + 75/100 = 6 3/4

The answer is "6 3/4"

Converting a Decimal to a Fraction : The decimal is represented in its equivalent fraction form and the fraction is simplified.

slide-show version coming soon