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Convert simple decimals into fractions

The learner understands that a terminating decimal represents a fraction whose denominator is a power of ten: tenths, hundredths, or thousandths correspond to denominators of 10, 100, or 1,000, with the decimal digits forming the numerator according to place value. The fraction may be reduced to an equivalent simplest form; nonterminating decimals, repeating decimals, and more advanced generalizations are outside this scope.

Detailed Explanation: Convert simple decimals into fractions

A terminating decimal can be written as a fraction by using its place value.

  • One digit after the decimal point means tenths, so use a denominator of 1010.
  • Two digits means hundredths, so use a denominator of 100100.
  • Three digits means thousandths, so use a denominator of 1,0001{,}000.

Example: Convert 0.750.75 to a fraction.

  1. There are two digits after the decimal point, so the denominator is 100100:
0.75=751000.75=\frac{75}{100}
  1. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, 2525:
75÷25100÷25=34\frac{75\div25}{100\div25}=\frac{3}{4}

Therefore,

0.75=340.75=\frac{3}{4}

The decimal digits become the numerator, and the number of decimal places tells you the denominator.

Learn by doing: Convert simple decimals into fractions

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    Decimals to Fractions - Standard

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