Compute x = 5.1 x 0.075 x 365.

Step-by-step solution

1. 1

   Recognise the calculation. This is the simple-interest product $I=P\cdot r\cdot t$: a principal of $5.1$ (often in thousands or millions), a rate of $0.075=7.5\%$, and a term of $365$ days expressed in daily units. Knowing the context tells you the answer should be roughly $7.5\%$ of $5.1\times365$.

2. 2

   Multiply the two decimals first. Taking the small numbers together keeps the intermediate value manageable:

   $5.1\times0.075=0.3825$

   Check the decimal places: $51\times75=3825$, and $1+3=4$ decimal places, so $0.3825$ ✓.

3. 3

   Multiply by 365. Split it as $0.3825\times(300+65)$:

   $0.3825\times300=114.75,\qquad 0.3825\times65=24.8625$

   $114.75+24.8625=139.6125$

4. 4

   State the result.

   $x=139.6125$

   The answer has exactly four decimal places, inherited from the four in $0.3825$ multiplied by an integer.

5. 5

   Cross-check by reordering the factors. Multiplication is associative, so grouping differently must agree: $0.075\times365=27.375$, and $5.1\times27.375=139.6125$ ✓. Also $5.1\times365=1861.5$, and $1861.5\times0.075=139.6125$ ✓ — all three orderings match, confirming the value.