Find the vertical distance between these two points.

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chijioke

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The highest point on the earth surface is \(\displaystyle 8.848 × 10^3m\) above sea level. The lowest point on the earth's surface is \(\displaystyle 1.103 × 10^4m\) below sea level. Find the vertical distance between these two points. Give your answer in standard form.

I am having a pictorial view of the problem like this:
IMG_20220905_084540.jpg
I am looking at it as if I am being asked to find difference between the two heights.
Solution
\(\displaystyle 8.848 × 10^3 - 1.103 × 10^4=\)
\(\displaystyle 10^3(8.848 - 1.103 × 10)=\)
\(\displaystyle 10^3(8.848 - 11.03)\)
\(\displaystyle 10^3(-2.182)\)
\(\displaystyle -2.182 × 10^3\)
I am not sure if what I did is correct because am having a negative solution. Please help him confirm if did the right thing. Thank you.
 
You actually need to add them together, not subtract. Think about it: If you had to find the distance between 3m above sea level and 2 m below sea level, would the distance be 1m or 5m?

Your method of factorising out the 10^3 is correct.
 
chijioke said:
The highest point on the earth surface is \(\displaystyle 8.848 × 10^3m\) above sea level. The lowest point on the earth's surface is \(\displaystyle 1.103 × 10^4m\) below sea level. Find the vertical distance between these two points. Give your answer in standard form.

I am having a pictorial view of the problem like this:
View attachment 33953
I am looking at it as if I am being asked to find difference between the two heights.
Solution
\(\displaystyle 8.848 × 10^3 - 1.103 × 10^4=\)
\(\displaystyle 10^3(8.848 - 1.103 × 10)=\)
\(\displaystyle 10^3(8.848 - 11.03)\)
\(\displaystyle 10^3(-2.182)\)
\(\displaystyle -2.182 × 10^3\)
I am not sure if what I did is correct because am having a negative solution. Please help him confirm if did the right thing. Thank you.
Click to expand...
I hope this isn't going to confuse you!

Yes, to find the difference in height between two levels you need to subtract. But the second measurement is below our zero point... sea level, so the second level is actually [imath]-1.103 \times 10^4[/imath] m. So the height difference would be
[imath]8.848 \times 10^3 - (-)1.103 \times 10^4 = 8.848 \times 10^3 + 1.103 \times 10^4[/imath] m

So as Harry_the_cat says, you add the two numbers in this case.

-Dan
 
I just have to say this, otherwise I will not feel good.
Sometimes to do a subtraction problem you need to subtract and other times you need to add. None-the-less it IS a subtraction problem!
The height above sea level will be represented by a positive number and the height below sea level will be represented by a NEGATIVE number. Now you need to subtract these two number.
 
topsquark said:
I hope this isn't going to confuse you!

Yes, to find the difference in height between two levels you need to subtract. But the second measurement is below our zero point... sea level, so the second level is actually [imath]-1.103 \times 10^4[/imath] m. So the height difference would be
[imath]8.848 \times 10^3 - (-)1.103 \times 10^4 = 8.848 \times 10^3 + 1.103 \times 10^4[/imath] m

So as Harry_the_cat says, you add the two numbers in this case.

-Dan
Click to expand...
Ya. Now I understand. But why didn't they show height below sea level as negative in wording. As in
The highest point on the earth surface is \(\displaystyle 8.848 × 10^3m\) above sea level. The lowest point on the earth's surface is \(\displaystyle -1.103 × 10^4m\) below sea level. Find the vertical distance between these two points. Give your answer in standard form.
Don't you think the wording is wrong in away?
Harry_the_cat said:
You actually need to add the together not subtract.
Click to expand...
I got it now.
Harry_the_cat said:
Think about it: If you had to find the distance between 3m above sea level and 2 m below sea level, would the distance be 1m or 5m?
Click to expand...
Going with what topsquark rightly pointed out, the distance between 3m above sea level and 2m below sea would be
[imath] \begin{array}{ll} 3m - (-2m)= \\ 3m + 2m = 5m \end{array}[/imath]
since the height (-2m) is negative.
Harry_the_cat said:
Your method of factorising out the 10^3 is correct.
Click to expand...
Thank you.
Steven G said:
None-the-less it IS a subtraction problem!
.
Click to expand...
Which one is IS a subtraction problem?Am interested in knowing. Please make me understand.
 
chijioke said:
But why didn't they show height below sea level as negative in wording. As in
The highest point on the earth surface is \(\displaystyle 8.848 × 10^3m\) above sea level. The lowest point on the earth's surface is \(\displaystyle -1.103 × 10^4m\) below sea level. Find the vertical distance between these two points. Give your answer in standard form.
Don't you think the wording is wrong in a way?
Click to expand...
No. You should only say once that it is negative. If something is -5 m above sea level, then it is 5 m below sea level! If it is -5 m below sea level, then it is 5 m above sea level! The word "below" tells you to go down; it's equivalent to using a negative number. Using both is a "double negative", and the meaning reverts to positive.

That is, if something is 5 m below sea level, then its altitude is -5 m; there, the negative sign takes the place of "below".

When they say "below", they are saying in wording that it is negative.

chijioke said:
Which one IS a subtraction problem? Am interested in knowing. Please make me understand.
Click to expand...
To add a negative number, you subtract its absolute value. So an addition of a negative is equivalent to a subtraction of a positive. They are the same "problem" written in different ways.
 
chijioke said:
Ya. Now I understand. But why didn't they show height below sea level as negative in wording. As in
The highest point on the earth surface is \(\displaystyle 8.848 × 10^3m\) above sea level. The lowest point on the earth's surface is \(\displaystyle -1.103 × 10^4m\) below sea level. Find the vertical distance between these two points. Give your answer in standard form.
Don't you think the wording is wrong in away?

I got it now.

Going with what topsquark rightly pointed out, the distance between 3m above sea level and 2m below sea would be
[imath] \begin{array}{ll} 3m - (-2m)= \\ 3m + 2m = 5m \end{array}[/imath]
since the height (-2m) is negative.

Thank you.

Which one is IS a subtraction problem?Am interested in knowing. Please make me understand.
Click to expand...
The subtraction problem is finding the distance between the highest point and the lowest point. A vertical distance is also calculated by the ( highest point - lowest point). If one or both of these numbers are negative, then they're negative. You still have to subtract them.
 
chijioke said:
Which one is IS a subtraction problem?Am interested in knowing. Please make me understand.
Click to expand...
The subtraction problem is finding the distance between the highest point and the lowest point. A vertical distance is also calculated by the ( highest point - lowest point). If one or both of these numbers are negative, then they're negative. You still have to subtract them.
 
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