Answer

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**Hint:**We will solve the given expression by converting the numbers as well as the decimal numbers into multiples of 10, if possible. So, the number of digits appearing after the decimal in the given question is 2 ,so, we will be multiplying and dividing the number 678.24 by 100. The expression obtained is further evaluated with respect to the fraction and we obtain the final result as 904.32.

**Complete step-by-step solution:**

According to the question we are to multiply \[\dfrac{4}{3}\times 678.24\] and we will try doing it in the easiest possible way.

Since we know that decimal numbers get complicated during calculation, so we will try to remove or at least separate the decimals during our calculation so that we don’t get confused and produce wrong answers.

So we will first deal with the decimal number in the question, which is, \[678.24\]

The expression we have, \[\dfrac{4}{3}\times 678.24\] will be modified in such a way that the decimal type gets removed during the calculation process.

We will multiply and divide by 100, and we know that there will not be any change as same number is multiplied and divided which is as follows:

\[\Rightarrow \dfrac{4}{3}\times 678.24\times \dfrac{100}{100}\]

So if we multiply \[678.24\] by \[100\] we can get rid of the decimal point.

Now we have,

\[\Rightarrow \dfrac{4}{3}\times \dfrac{67824}{100}\]

We need to check if \[67824\] is divisible by 3 or not. To check if a number is divisible by 3, we need to add the individual digits and if the sum is divisible by 3, then the number is divisible by 3.

Adding up the digits, we have,

\[6+7+8+2+4=27\] which is divisible by 3, therefore \[67824\] is divisible by 3.

Dividing the number by 32, we now have

\[\Rightarrow 4\times \dfrac{22608}{100}\]

Now multiplying \[4\times 22608\], we have

\[\Rightarrow \dfrac{4\times 22608}{100}\]

\[\Rightarrow \dfrac{90432}{100}\]

\[\Rightarrow 904.32\]

**Therefore, we get the answer as \[\Rightarrow 904.32\]**

**Note:**The multiplication operation should be done step-wise to prevent any errors. Conditions for divisibility of numbers from 1 - 10 should be well versed with to fasten the calculation. If the denominator has 10 or its multiple then it should not be disturbed and only needs to be attended at the very end, like how we solved in the above answer.

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