Final answer:
To estimate 42.4 ÷ 7.28, we can round to 42 and 7 respectively, yielding an estimated quotient of 6. This quick estimation is close to the actual value and highlights the importance of considering significant figures, especially in precise calculations.
Step-by-step explanation:
To estimate the quotient of 42.4 ÷ 7.28, we can round these numbers to make the division simpler. We can approximate 42.4 as 42 (or 40 if we want a rounder number) and 7.28 as 7. If we use these rounded numbers, we get:
42 ÷ 7 = 6
Since we rounded down the dividend and rounded down the divisor, our estimate should be fairly close to the true value. Calculators are precise, but they do not consider the significant figures and their relevance in a real-world context. Hence, while a calculator might give a more precise answer, like the provided sample calculations, estimating can give us a quick, rough understanding of what the result should be around.
For example, when dividing 543.3 by (19.0/100) or other similar operations, we would follow the division normally but might need to round the answer appropriately based on significant figures.
Thus, our estimated quotient for 42.4 ÷ 7.28 would be 6, recognising that the true answer would be slightly more since we've rounded both numbers down. In actual calculations, especially for more critical applications, one would use the exact numbers and take significant figures into account when reporting the final value.