Monday, 20 April 2009

Reciprocal of a decimal

Next we'll look at the reciprocal of a decimal. As an example, what is the reciprocal of 0.6?

The reciprocal of a number is what you'd have to multiply it by to get 1. For a fraction, we can get the reciprocal by swapping the numerator and the denominator. For instance, the reciprocal of 6/10 is 10/6. This is because when we multiply 6/10 by 10/6 we get 60/60, and that equals 1. Anything divided by itself equals 1.

For a decimal, the easiest way to calculate the reciprocal is to convert it to a fraction first. So, 0.6 is the same as 6/10, and we just worked out that the reciprocal of that is 10/6.

We will probably want to convert the answer to a decimal, so that it matches the number we started with. To do this we convert first to a mixed number, by subtracting the denominator from the numerator as many times as we can. 10/6 = 1 4/6 because we can subtract the 6 from the 10 once, with a remainder of 4. We can simplify the 4/6 to 2/3. As a decimal this is 0.666..., where the ... shows that the 6 is recurring - the row of sixes never actually ends. Finally, we add the whole number part of the mixed number to this decimal, to give us 1.666... If we wanted this to just two decimal places, then it would be written as 1.67, because 1.666 recurring is closer to 1.67 than it is to 1.66.

That sums it up.

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