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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.continue
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.



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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 decimaldivision to convert fraction to 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.division to convert fraction to decimal 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, division

Convert `35/2` into decimal.

  • `0.175`
  • `17.5`
  • `17.5`

The answer is "`17.5`".

By long division method, division

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.

                            
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