Mathematics units

[lev888]

Hi guys, whenever I have sec/sec then sec/sec=1
what's confusing me, how from splitting units we get number?! I mean we don't have numbers ..so how we get number?! really weird magic

It takes John 20 seconds to post a question on a forum. How many questions can he post in 60 seconds?
60sec/20sec = 3. Units cancel, just the number remains.

 

[topsquark]

WHAAAAT?????????????????????????????????????????????????????????????! impossible, so 1 is a magic?

1 is not magic. In the context of units it is simply a notation for something unitless. \(\displaystyle 1 \times 3 = 3\). Does this make "1" magical?

-Dan

 

[Otis]

… I have sec/sec then sec/sec=1

what's confusing me … we don't have numbers …

What are you looking at?

Please post a specific exercise statement.

 

[Ryan$]

Hi guys, my teacher said that if we want to write 10 cm in terms of meters, then we do 10cm/100 = 0.1m . why is that true to do divide by meters for converting cm to meters?! I mean "in terms of" what does it mean in more simple words?!

I find it hard and sorry in advance for that, I know it's basic questions but I already explained my issues with math and my mind.


thanks alot .

 

[Ryan$]

if someone said to me 100cm, and the other person said to me 1m, are it's the same meaning ? if so how is that really right? what's confusing me, the "100 cm" is physically a specific amount , but how much that specific amount? is it number?!

 

[Otis]

… why is that true to … divide by meters for converting cm to meters?

You're not dividing by meters. You're dividing by 100.

The definition of 'centimeter' is the reason why we divide by 100. Look up the definition. What is the relationship between a centimeter and a meter?

… "in terms of" what does it mean in more simple words?

You already said what it means, above. Expressing centimeters in terms of meters means: convert centimeters to meters.

\(\;\)

 

[Otis]

… how is [100 cm = 1 m] really right? …

Because that's the relationship which defines 'centimeter'.

Are you trying to argue that we can't accept the given definition?

? Please look up definitions before you post about them.

\(\;\)

 

[ksdhart2]

You're not dividing by meters, you're dividing by 100. This is simply a number. Nothing more, nothing less, no units attached to it. To see why this is the appropriate thing to do, let's consider your goal. Your goal is to convert 10 centimeters into meters. In mathematics, we use the equals sign to mean "has the same value as," so we can write an equation:

\(\displaystyle 10 \text{ cm} = (???) \text{ m}\)

We know a relationship between centimeters and meters that can help us out here. We know that 100 centimeters is equivalent to 1 meter. We wrote it using different words, but those two quantities are exactly the same. Since you seem to have trouble with symbolic representation and/or a deep distrust of anything told to you, you can always verify this yourself. Find a meter stick. This is, by definition, one meter long. Most meter sticks have markings on them subdividing the measurement into centimeters. Count up each individual "centimeter" mark. How many are there? Based on this, how many centimeters long is the meter stick? Since these two measurements must, clearly, refer to the exact same physical length (i.e. the length of the meter stick didn't change while you were counting the marks), 100 centimeters must be the exact same thing as 1 meter.

Now how we can use this relationship? Well, we also know three things that are always true:

\(\displaystyle \frac{\text{(Something)}}{\text{(That Same Thing)}} = 1\)

\(\displaystyle (\text{Something}) \times 1 = \text{(Something)}\)

\(\displaystyle \frac{\text{Something}}{1}= \text{(Something)}\)

Can you see why we can use these three facts to rewrite our original equation as:

\(\displaystyle \frac{10 \text{ cm}}{1} \times \frac{1 \text{ m}}{100 \text{ cm}} = (???) \text{ m}\)

Then, multiplying the fractions straight across as per the usual rules, we get:

\(\displaystyle \frac{10 \cancel{\text{ cm}}}{1} \times \frac{1 \text{ m}}{100 \cancel{\text{ cm}}} = (???) \text{ m}\)

\(\displaystyle 10 \text{ cm} = \frac{10 \text{ m}}{100} = 0.1 \text{ m}\)

 

[Ryan$]

You're not dividing by meters. You're dividing by 100.

The definition of 'centimeter' is the reason why we divide by 100. Look up the definition. What is the relationship between a centimeter and a meter?


You already said what it means, above. Expressing centimeters in terms of meters means: convert centimeters to meters.

\(\;\)

but how much is 1cm ? I mean in terms of amounts, how much? .. isn't 1cm a number/amount at the end? if so then, what's that amount/number?

 

[JeffM]

Ryan, you make things so difficult for yourself. The letters cm here are not variables; they are an abbreviation of the word "centimeters."

 

[Otis]

… how much is 1cm ? …

Did you look at the definition, yet? Like all other units of length, a centimeter is defined by comparing it to a known length. We know how long a meter is.

1 cm is defined as one-hundredth of a meter.

We can convert 1 cm to other units, too. In terms of decimeters, 1 cm is a tenth of a decimeter.

1 cm is 10 millimeters.

Give us a unit of length that you can accept, and we will tell you how many centimeters that length is.

If you need a visual reference, buy a ruler marked in millimeters and centimeters. You will then see how much 1 cm is (10 mm), and don't worry about exactness. Just accept what you see on the ruler and the definition(s) you look up.

… [is] 1cm a number/amount at the end? …

Do you mean "at the end of the day", so to speak? If so, then 'yes'. The number of centimeters in a length of 1 cm is one. The amount of length is 1/100th of a meter (or ten mm, or 1/10th dm, etc).

?

 

[Ryan$]

Did you look at the definition, yet? Like all other units of length, a centimeter is defined by comparing it to a known length. We know how long a meter is.

1 cm is defined as one-hundredth of a meter.

We can convert 1 cm to other units, too. In terms of decimeters, 1 cm is a tenth of a decimeter.

1 cm is 10 millimeters.

Give us a unit of length that you can accept, and we will tell you how many centimeters that length is.

If you need a visual reference, buy a ruler marked in millimeters and centimeters. You will then see how much 1 cm is (10 mm), and don't worry about exactness. Just accept what you see on the ruler and the definition(s) you look up.


Do you mean "at the end of the day", so to speak? If so, then 'yes'. The number of centimeters in a length of 1 cm is one. The amount of length is 1/100th of a meter (or ten mm, or 1/10th dm, etc).

?

but it's not acceptable for me how dividing is giving us the answer "in terms of " .. doesn't make sense for me ... may please elaborate more about the dividing concept and how it's related to in terms of?!


why not for example doing "*" for answering "in terms of" questions ?!

 

[Otis]

… please elaborate more about the dividing concept …

… why not for example [do multiplication instead]?

Ryan, dividing by 100 is the same as multiplying by 1/100.

Go back to post #5, and study the multiplications shown by ksdhart2. He multiplied 10 cm by a conversion factor, to convert 10 cm to meters. The final answer expresses 10 cm in terms of meters.

\(\displaystyle \displaystyle \frac{10 \cancel{\text{ cm}}}{1} \times \frac{1 \text{ m}}{100 \cancel{\text{ cm}}} = \frac{1}{10} \text{ m}\)

Dividing 10 by 100 is the same as multiplying 10/1 by 1/100.

?

 

[Ryan$]

but how the concept of "dividing" give as the concept of "in terms of " ?! doesn't make sense for me

 

[Dr.Peterson]

What you are calling "in terms of" would better be stated as "how many".

Your question, "write 10 cm in terms of meters" means, "10 cm is equal to how many meters?"

"How many" is exactly the question division answers. "How many 3's are equal to 6?" means 3 times what equals 6, and the answer is 6 divided by 3, namely 2.

How many meters in 10 cm? Well, each meter is 100 centimeters, so you are asking how many 100's of centimeters make 10 centimeters; that is, 100 times what = 10. We divide 10 by 100, and get 0.1.

 

[Otis]

but how the concept of "dividing" give as the concept of "in terms of " ?! doesn't make sense for me

Oh, the instruction 'in terms of' is not always related to division. That's only in this exercise (and others like it).

In terms of meters just means they want you to express 1 cm as meters. Division (or multiplication by the reciprocal) is how we do that.

You will see the phrase 'in terms of' used in other exercises that have nothing to do with division. 'In terms of' tells you what form the answer needs to be OR what information they specifically want described (see the last example, below).

Here are some examples:

Given that \(y = \frac{2}{x - 3}\), express x in terms of y. It means they want \(x = \frac{2}{y} + 3\). In other words, they want an expression for x that contains y.

Write \(\sqrt{-4}\) in terms of i. It means they want 2i. In other words, an expression for \(\sqrt{-4}\) that contains i.

Express \(\sqrt{3}\) in terms of a rational exponent. It means they want \(3^{1/2}\). That is, an expression for \(\sqrt{3}\) that contains a rational exponent.

The graph of y = mx + b is a straight line. Interpret the number b, in terms of the graph. In this case, they want us to say that (0,b) is the y-intercept. That is, the point on the y-axis where the graph crosses.

So you see that 'in terms of' doesn't tell us what to do (like division) so much as telling us what form the result needs to be (like some number of meters).

?

 

[Ryan$]

What you are calling "in terms of" would better be stated as "how many".

Your question, "write 10 cm in terms of meters" means, "10 cm is equal to how many meters?"

"How many" is exactly the question division answers. "How many 3's are equal to 6?" means 3 times what equals 6, and the answer is 6 divided by 3, namely 2.

How many meters in 10 cm? Well, each meter is 100 centimeters, so you are asking how many 100's of centimeters make 10 centimeters; that is, 100 times what = 10. We divide 10 by 100, and get 0.1.

but if we get at the end the answer of "how many" is number , so how we say it's number of meters or whatever or divide we say it's a number of what we divide? I mean if the answer if "how many" is number, then how we say that number as a unit of what we divide?! 100cm to meters , for answering how many 100cm to 1memters is 1, but how we say it's 1 meter, I mean "1" with units [meter] who said that unit is meter/what type of we divide?!

 

[ksdhart2]

Look, I'll be honest with you here. One of the abilities I pride myself on is that I'm skilled at reading between the lines and parsing what often amounts to gibberish, and figuring what students are really asking. But... I got nothing this time. I literally don't even know what you're asking or what you're confused by.

 

[mmm4444bot]

… if we get … the answer of "how many" … how [can] we say [that it's a] number of meters or whatever …

We get the units from the context in the specific exercise.

… who said [the] unit is meter …

Whoever wrote the exercise.

You're going around in circles, Ryan. These questions have already been answered. I think you could be confusing yourself because you're mixing together different exercises in your mind and thinking that interpretations which arise in one exercise must apply to all exercises. You need to focus on one exercise at a time and tell us what it is. We can help you, if you provide the exercise statement. (Let's separate your discussions by specific exercise (i.e., start a new thread by posting a new exercise statement.)

?

 

[Old Engineer]

Ryan$,
Here's how I think you have been confused. You have a length of 10 cm that you want to describe "in terms of" meters. Several writers suggested that you divide by one hundred. But you know that if you divide by one hundred you get something much smaller than what you started with. You are absolutely correct. If you want the answer to be the same thing you started with, the only thing you can multiply or divide by is 1. The trick is in knowing how to do that so as to change units.

Here's the trick: Anything divided by itself is 1. For this problem I am interested in M and cm. We know that 1 M = 100 cm That is 1 M and 100 cm are the same thing. So, 1 M / 100 cm = 1 also 100 cm / 1 M = 1
To express 10 cm in terms of M I will multiply 10 cm by one of these.
Try 10 cm * 1 M / 100 cm simplify to 10 cm * M / 100 cm 10/100 = 0.1 cm/cm = 1 leaving 0.1 M This is our answer.

(The other expression 10 cm * 100 cm / 1M gives us 1000 cm sq / M which is not very useful, so we ignore it.)

The point is: for all "in terms of" or units problems you multiply by 1, written as a relationship between the units you want to convert. Multiply by 1 does not change your physical value. The "divide by 100" or whatever is just the arithmetic of simplifying that expression.

I was saddened to see your thread cut off before you received a clear answer.

(Moderator Note: Thread reopened to merge subsequent, duplicated discussions started by the OP)