The number 0.166 recurring where the 166 recurs forever is expressed as a fraction 166/999 or one hundred and sixty-six nine hundred and ninety-ninths.
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Multiply by the smallest integral power of 10 to produce an integer from the original number, then use the resulting integer over the power of ten as a fraction. In this specific instance, 4.64 = 464/100 or in lowest terms 116/25.
When multiplying fractions we multiply all the numerators to produce a new numerator and we multiply all the denominators to produce a new denominator, then we reduce the new fraction to its simplest form. In this case - 7/8 x 2/5 gives 7 x 2 = 14 as the new numerator and 8 x 5 = 40 as the new denominator The "new" fraction is now 14/40 or 7/20
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