I have to convert inches to 250 cm.My book states the expression to calculate this as 250 cm x 1in/2.54 cm. I followed through to divide, and got 98.425, which following the rules of significantdigits, would equal 98, right? 250 only has 2 sig digs, it'd have to be 98. But my book says its 98.4. How can this be?
I think your book is counting 250 cm as 250. cm. which makes 3 s.f. and that's how they obtained 98.4. You're right, however, that 250, written that way, has only two s.f.
To convert inches to centimeters, you can use the conversion factor 1 inch = 2.54 cm.
Let's break down the expression provided in your book:
250 cm x (1 in / 2.54 cm)
When you divide 250 cm by 2.54 cm, you correctly get 98.425.
Now, let's discuss significant figures. Significant figures are used to indicate the precision of a measurement. In this case, the number 250 cm has two significant figures because it is given as a whole number.
According to the rules of significant figures, when you perform calculations, the result should have the same number of significant figures as the least precise measurement used in the calculation.
In this case, since 250 cm has two significant figures, the result should also have two significant figures. Therefore, your initial assumption that the answer is 98 is correct.
However, your book states the answer as 98.4, which seems contradictory.
To resolve this discrepancy, we need to consider the concept of rounding. When performing calculations with significant figures, you usually round the final answer to the appropriate decimal place based on the least precise measurement.
In this case, the least precise measurement is the 250 cm, which has two significant figures. 98.425 has five decimal places, exceeding the precision of the original measurement. Therefore, according to significant figures and rounding rules, the result can be rounded to two significant figures, giving us 98.
It seems that your book has followed a different rounding rule and rounded to one decimal place. Although this is not the standard approach, rounding to one decimal place would yield the answer of 98.4 in this case.
Ultimately, it's important to note that rounding rules may vary depending on the context and the requirements of specific calculations.