Question

f femto = 10^-15
p pico = 10^-12
n nano= 10^-9
micro = 10^-6
m milli = 10^-3
c centi= 10^-2
d deci = 10^-1
k kilo= 10^3
M mega= 10^6
G giga= 10^9
T tera= 10^12
P peta= 10^15
E exa= 10^18

So this is the chart I have basically. I just want to know how could I possibly use this information to give me answers to questions like this...

38m = __mm

Answer 1

The first little m in mm means milli which is a symbol that means one-one thousandth.

Answer 2

So you can think of it like an equation (because it is one) like
\[38*m = \frac{x}{1000}*m\]

Answer 3

you can replace the x/1000 with 10^-3 * x to stay consistent with your chart as well.

Answer 4

38m = 10^-3m/1000 ? OR 38M = 10^-3?

Answer 5

38m = x*10^-3 m.
The m's cancel on each side since you're just solving for a number irrespective of the units, so x = 38 ÷ 10^-3

Answer 6

Essentially, you're just replacing the m that means milli with 10^-3 and the units cancel out leaving you just to solve for how many of the little things fit inside the big thing.

Answer 7

So I can just type that in my calculator? 38/10^-3?

Answer 8

Sure, depending on your calculator you might want to use extra parentheses, but also consider that dividing by 10^-3 is the same as multiplying by 1000.

Answer 9

Okay they both gave me the same answer. So I'll just type it in like 38/10^-3... so would 38000 be my answer?

Answer 10

Then you can do a reality check: meters are long, and millimeters are really short, so it makes sense that it takes a whole lot of very short things to make one long thing.

Answer 11

okay so 38,000mm equals 38m

Answer 12

You can either express your answer as x=38000, or you can put it back into the original statement and claim that 38m = 38000mm.

Answer 13

I'm sorry... its just this stuff seems hard

Answer 14

Another example: Say you're going from cL, centiliters to µL, microliters.
c, centi, is 10^-2 and µ, micro, is 10^-6, so let's say you start with 50cL. The equation is:
50cL = xµL. Change the c and the µ to 10^-2 and 10^-6 and you get:
50*10^-2 L = x*10^-6 L.

Answer 15

Can I do another one and I want to see if I can get the answer and you check it?

Answer 16

But you don't always have to look so fancy with it. 10^-2 just means divide by 100, and 10^-6 means to divide by 1,000,000.
So (50 ÷ 100) = (x ÷ 1,000,000).
It's a proportion, so you can cross-multiply to solve.

Answer 17

Okay, so I am going to try and solve this:
312.5cm = ___m

Now, first you said it is a proportion right? How is that a proportion though? They didn't give me two fractions?

Answer 18

Based off of my chart... I guess I can type in my calculator 312.5 * 10^-2

Answer 19

But they are fractions!

Answer 20

\[c, \space centi, \space = \frac{1}{100}\]

Answer 21

ok

Answer 22

You could also do 312.5 ÷ 100. ;-)

Answer 23

(two fewer key strokes)

Answer 24

Okay so I would have first

312.5cm = X meters
-------- = 3.125m
100cm

Answer 25

So is this it?

Answer 26

that simple?

Answer 27

The notation is a little wonky, but you obviously get the idea. Yes, that simple.

Answer 28

one more

Answer 29

A good way to get an intuitive feel for it is to get an actual meter stick and compare the sizes of the meter, centimeter, and millimeter.

Answer 30

1km = ___mm

Answer 31

1km = 1000 meters

Answer 32

1km = Xmm
------ = ?
1000km

Answer 33

@CliffSedge now this one I think is wrong... because I'm getting the answer... 0.001

Answer 34

Yeah, I think you went in the opposite direction.

Answer 35

A kilometer is very long (compared to a meter), and a millimeter is very short (compared to a meter), so you'd expect a kilometer to contain a very large number of millimeters.

Answer 36

You can either solve this as a proportion equation or do a two-step unit conversion.
Option 1.
\[1 \space km = X \space mm \rightarrow 1 \times 10^3 \space m = X \times 10^{-3} \space m\]
Option 2.
\[1 \space km \cdot \frac{1000m}{1km} = 1000m \rightarrow 1000m \cdot \frac{1000mm}{1m} \space = X\]

Answer 37

Okay ... so I got 1,000,000

Answer 38

10^6

Answer 39

Yep, it takes one million millimeters to make one kilometer.

Answer 40

oh ok

Answer 41

Getting the hang of it?

Answer 42

Yeah, I think so.... if a problem arises I'll open a question