The number 3.07 × 10 -4 written in standard form is _____.
2 answers:
Answer:
0.000307
Step-by-step explanation:
<h2>The most important parts of my explanation are written in bold. You can just read those parts if you're in a hurry!</h2>The first step I do when figuring out these type of questions is finding out which way we're going to be moving our decimal; Right or left?
We can quickly find out the answer by looking at whether the index is positive or negative. The index is the small number just next to the 10.
In this case, the index is negative. We can tell by the minus sign in front of it, which means it's a negative number. When the index is a negative, it means you're going to be moving your decimal to the right, AKA your number is going to get smaller.
Now all we need to know is how many spaces to the right the decimal needs to move. Again, this answer comes from the index. The number written in as the index is -4. We already know what the - means, so we can just look at the number as 4 on its own.
The index tells us that the decimal needs to be moved 4 places to the right. So that's just what we do!
3.07 ↓
0.307 ↓
0.0307 ↓
0.00307 ↓
0.000307
Moving the decimal 4 places to the right gives us the number 0.000307, which means;
The number ×
written in standard form is <u>Option B, 0.000307</u>.
You might be interested in
Answer:
72 feet from the shorter pole
Step-by-step explanation:
The anchor point that minimizes the total wire length is one that divides the distance between the poles in the same proportion as the pole heights. That is, the two created triangles will be similar.
The shorter pole height as a fraction of the total pole height is ...
18/(18+24) = 3/7
so the anchor distance from the shorter pole as a fraction of the total distance between poles will be the same:
d/168 = 3/7
d = 168·(3/7) = 72
The wire should be anchored 72 feet from the 18 ft pole.
_____
<em>Comment on the problem</em>
This is equivalent to asking, "where do I place a mirror on the ground so I can see the top of the other pole by looking in the mirror from the top of one pole?" Such a question is answered by reflecting one pole across the plane of the ground and drawing a straight line from its image location to the top of the other pole. Where the line intersects the plane of the ground is where the mirror (or anchor point) should be placed. The "similar triangle" description above is essentially the same approach.
__
Alternatively, you can write an equation for the length (L) of the wire as a function of the location of the anchor point:
L = √(18²+x²) + √(24² +(168-x)²)
and then differentiate with respect to x and find the value that makes the derivative zero. That seems much more complicated and error-prone, but it gives the same answer.
