First it is important to understand what a reciprocal is. The reciprocal of any number x is the number 1/x. The reciprocal of a number is also its multiplicative inverse, which means that the number times its reciprocal must equal 1. For a number such as 2, the reciprocal would be 1/2. For a fraction such as 2/5, the reciprocal would be 5/2.
Finding the reciprocal of a decimal can be done in a number of ways.
- Change the decimal to a fraction first.
Ex. 0.25 is 25/100 and is equivalent to the fraction 1/4. Therefore Its reciprocal
would be 4/1 or 4.
- Keep the decimal and form the fraction 1/?? which can then be or converted to a
Ex. 0.75 The reciprocal is 1/0.75. Using a calculator, the decimal form can be found by performing the operation: 1 divided by 0.75. The decimal reciprocal in
this case is a repeating decimal, 1.33333....
After finding a reciprocal of a number, perform a quick check by multiplying your original number and the reciprocal to determine that the product is 1:
- (0.25)(4) = 1.00
- (0.75)(1.33....) = 1 but it is easier to see for sure with repeating decimals if you use the fractions instead of the decimals.
(3/4)(4/3) = 12/12 = 1
Hope this helps,