Would '0' be counted as a decimal place when rounding off?

Question

For example, the first question asks you to round 15.2mm to cm, and that is 0.152cm.
The second question asks to convert 15.2mm to m, which is 0.0152m.
THe last question asks you to convert 15.2mm to km, and that would be 0.0000152km.

The question also asks for the answers to each question to be rounded off to 3 decimal places. I know that the first question is already rounded off to 3dp, but I am confused about the others. I thought that zeros had to be counted as a decimal place, but I'm not quite sure. The answers in the answer book for these questions are the answers from above, so I'm presuming that the answer book is saying that zeros do not count as a decimal place. Please help. Thanks.

Answer 1

YES because the 0 is still a "place holder" just

like any other difit

Answer 2

Yes, three decimal places means just that - three decimals.



Correct with the first one.



The secnd one is 0.015 to three places.



And the third one is 0.000 km. Which is common sense when you think about it. If someone asks you how many kilometers is 15 mm, the answer is zero to a high degree of accuracy.

[ However, the answer 0.0000152 is correct to "three significant figures", which is a completely different matter. ]



If asked for your waist size, you wouldn't answer in kilometers, would you ? But if you WERE asked for it in kilometers to the nearest thousandth km (that is, 3 decimal places), the answer would be zero, because I shouldn't think that your waist measurement is anything near 1 metre, is it ?



We normally choose units which are appropriate to the actual size of the thing being measured. And the stated accuracy of the measurement likewise corresponds in some degree to the actual measurement. If you have to quote it in inappropriate units, then the number of places is probably inappropriate as well.

Answer 3

When rounding off to a number of decimal places, you count the zeros

So 15.200 mm = 1.520 cm = 0.015m = 0.000 km.



However, if you are working to three significant figures:

15.2 mm = 1.52 cm = 0.0152 m = 0.0000152 km



Notice the difference between the two 'exercises' - one is 3 decimal places, and the other is 3 significant figures.

Answer 4

Hi,



When rounding off.. 0s as you are saying are to be counted.



0.0152 has to be rounded off to 0.015 for 3dp and 0.02 for 2dp



Can't say how is the book you're referring calculating the answer or if the question has more parts to it

Answer 5

of course zeros are to be counted as decimals.. 1km = 0.001meters.. the decimal point was moved three decimal places..