Question

2.48925 C : 3.9901 H : 1.000 O

The ratio does not give whole
numbers, so we have to use a
multiplier. What can we multiply each element by in order to have them all reach the smallest whole number?

multiply by [?]

Hint: The multiplier should be a whole number.

Answer 1

20,000

Explanation:

You want the multiplier of {2.48925, 3.9901, 1.000} that will make each of these numbers a whole number.

Multiplier

We know that we can multiply the numbers by 10^5 to make them whole numbers. However, we observe that doing so will give a set of numbers that are multiples of 5. This means we can multiply by (10^5)/5 = 20,000 to make the ratio be the smallest whole numbers.

20,000 × {2.48925, 3.9901, 1.000} = {49785, 79802, 20000}

The smallest multiplier will be 20,000.

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Additional comment

Effectively, we found that the greatest common divisor of these numbers is 0.00005, and we divided by that. We usually work with integers to find the GCD, but the algorithms work just as well for fractions or decimal numbers.

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