Figuring out decimals, PLEASE help

[Mermaid500]

My 10 year old needs to write the answers in decimal form.

I do understand the place values and I have taught her them. She has a pretty good grasp of it. I am trying to prepare for tomorrows lesson and I am so confused. If you could even give me a website that might explain it, that would be very helpful and very much appreciated.

So how do I tell her to write a decimal for 6 x 1 + 5 x 1/10? I my only idea is, other than 6 x 1 = 6 +5 = 11 but what do I do to explain 11 x 1/10?

I am so lost, and it just gets harder. I have no clue what I am doing.

2 x 10 + 7 x 1/10 +3 x 1/100?
OK 2 x 10 =20 + 7 = 27 x 1/10 (?) = (?) + 3 = (?) x 1/100 = (?)

Please suggest any thing that will help me figure out what to tell her tomorrow, and how to learn to solve the problems myself.
Thank you in advance!!

 

[lev888]

My 10 year old needs to write the answers in decimal form.

I do understand the place values and I have taught her them. She has a pretty good grasp of it. I am trying to prepare for tomorrows lesson and I am so confused. If you could even give me a website that might explain it, that would be very helpful and very much appreciated.

So how do I tell her to write a decimal for 6 x 1 + 5 x 1/10? I my only idea is, other than 6 x 1 = 6 +5 = 11 but what do I do to explain 11 x 1/10?

I am so lost, and it just gets harder. I have no clue what I am doing.

2 x 10 + 7 x 1/10 +3 x 1/100?
OK 2 x 10 =20 + 7 = 27 x 1/10 (?) = (?) + 3 = (?) x 1/100 = (?)

Please suggest any thing that will help me figure out what to tell her tomorrow, and how to learn to solve the problems myself.
Thank you in advance!!

Does she have a textbook?

 

[Dr.Peterson]

My 10 year old needs to write the answers in decimal form.

I do understand the place values and I have taught her them. She has a pretty good grasp of it. I am trying to prepare for tomorrows lesson and I am so confused. If you could even give me a website that might explain it, that would be very helpful and very much appreciated.

So how do I tell her to write a decimal for 6 x 1 + 5 x 1/10? I my only idea is, other than 6 x 1 = 6 +5 = 11 but what do I do to explain 11 x 1/10?

I am so lost, and it just gets harder. I have no clue what I am doing.

2 x 10 + 7 x 1/10 +3 x 1/100?
OK 2 x 10 =20 + 7 = 27 x 1/10 (?) = (?) + 3 = (?) x 1/100 = (?)

Please suggest any thing that will help me figure out what to tell her tomorrow, and how to learn to solve the problems myself.
Thank you in advance!!

This is called expanded form (among other names), and is certainly closely related to place value, so I'm not sure what part of it you (two) are missing.

For 6 x 1 + 5 x 1/10, you are being told that the ones place is 6 and the tenths place is 5, so the number is 6.5. That is, 6 x 1 = 6, and 5 x 1/10 = 5 x 0.1 = 0.5, and their sum is 6.5. But I would think of it the first way.

In general, if you are given something like A x 1 + B x 1/10 + C x 1/100, you write it as A.BC.

You won't see 11 x 1/10 in this form, probably; if you did, that would be 1.1.

Again, 2 x 10 + 7 x 1/10 + 3 x 1/100 means 2 is in the tens place, 7 in the tenths place, and 3 in the hundredths place. Here they've skipped the ones place, so that gets a 0: 20.73. It's a good idea to check: there's 2 in the tens place, 0 in the ones place, 7 in the tenths place, and 3 in the hundredths place, which is all correct.

Possibly one thing you are missing is the "order of operations". In this example, before you add the 7, you have to do the multiplication. Think of it this way: 2 x 10 + 7 x 1/10 + 3 x 1/100. Each number is multiplied by a place value, so you think of them in pairs.

 

[Mermaid500]

Does she have a textbook?

I wish, sorry. Actually with distance learning this school year there is really no instruction, and they haven't even done a zoom meeting for the children either. The program the school is providing will change when they get access to something called Calvert. But until that happens us parents are on our own pretty much.

 

[Mermaid500]

This is called expanded form (among other names), and is certainly closely related to place value, so I'm not sure what part of it you (two) are missing.

For 6 x 1 + 5 x 1/10, you are being told that the ones place is 6 and the tenths place is 5, so the number is 6.5. That is, 6 x 1 = 6, and 5 x 1/10 = 5 x 0.1 = 0.5, and their sum is 6.5. But I would think of it the first way.

In general, if you are given something like A x 1 + B x 1/10 + C x 1/100, you write it as A.BC.

You won't see 11 x 1/10 in this form, probably; if you did, that would be 1.1.

Again, 2 x 10 + 7 x 1/10 + 3 x 1/100 means 2 is in the tens place, 7 in the tenths place, and 3 in the hundredths place. Here they've skipped the ones place, so that gets a 0: 20.73. It's a good idea to check: there's 2 in the tens place, 0 in the ones place, 7 in the tenths place, and 3 in the hundredths place, which is all correct.

Possibly one thing you are missing is the "order of operations". In this example, before you add the 7, you have to do the multiplication. Think of it this way: 2 x 10 + 7 x 1/10 + 3 x 1/100. Each number is multiplied by a place value, so you think of them in pairs.

Thank you. I see that you are an elite member and posted almost 12,000 messages.

I am not a high school graduate, and I am sure this explanation is very helpful to some. I am still confused, and do not know how to explain what you wrote to my 10 year old. I appreciate the response I really do,, I will try to re-read it and see if I can understand your explanation better.

Do you know of a website or youtube video that can maybe help me understand better Dr?

 

[Dr.Peterson]

I wish, sorry. Actually with distance learning this school year there is really no instruction, and they haven't even done a zoom meeting for the children either. The program the school is providing will change when they get access to something called Calvert. But until that happens us parents are on our own pretty much.

You mentioned a lesson; is that in written form, or a video, or what? Any materials you have could help us see how to best supplement it.

You can search for the term I gave you, "expanded form"; the trouble with that is that there are a couple slightly different versions of that, some probably at a higher level than you need, so you have to find a source that matches your need. Here is one that might do:

IXL | Writing decimals in expanded form

Learn how to write decimal numbers in expanded form! Walk through this quick and easy lesson for examples and practice problems to become a place value master.

www.ixl.com

 

[Mermaid500]

You mentioned a lesson; is that in written form, or a video, or what? Any materials you have could help us see how to best supplement it.

You can search for the term I gave you, "expanded form"; the trouble with that is that there are a couple slightly different versions of that, some probably at a higher level than you need, so you have to find a source that matches your need. Here is one that might do:

IXL | Writing decimals in expanded form

Learn how to write decimal numbers in expanded form! Walk through this quick and easy lesson for examples and practice problems to become a place value master.

www.ixl.com

I guess I shouldn't have used the word lesson. All she has is 4 pages to answer. No instruction at all.

That website helped A LOT. Thank you so much!

 

[HallsofIvy]

Be careful of the order of operations! To calculate 6x1+ 5x 1/10, do the multiplications first. 6x1= 6 and 5x 1/10= 5/10= 1/2. Now add- 6+ 1/2= 6 and a half or 6.5.

You do NOT add 6+ 5= 11 and then diviide by 2!

 

[Mermaid500]

Be careful of the order of operations! To calculate 6x1+ 5x 1/10, do the multiplications first. 6x1= 6 and 5x 1/10= 5/10= 1/2. Now add- 6+ 1/2= 6 and a half or 6.5.

You do NOT add 6+ 5= 11 and then diviide by 2!

Thank you!

 

[Otis]

Hi Mermaid. Has your daughter done the reverse, yet?

Try some whole numbers, first.

415 $\;$=$\;$ 4×100 $\;$+$\;$ 1×10 $\;$+$\;$ 5×1 $\;$=$\;$ 400 + 10 + 5 $\;$=$\;$ 415

370 $\;$=$\;$ 3×100 $\;$+$\;$ 7×10 $\;$+$\;$ 0×1 $\;$=$\;$ 300 + 70 + 0 $\;$=$\;$ 370

Then try some decimals.

2.1 $\;$=$\;$ 2×1 $\;$+$\;$ 1×$\frac{1}{10}$ $\;$=$\;$ 2 + $\frac{1}{10}$ $\;$=$\;$ 2.1

0.6 $\;$=$\;$ 0×1 $\;$+$\;$ 6×$\frac{1}{10}$ $\;$=$\;$ 0 + $\frac{6}{10}$ $\;$=$\;$ 0.6

3.09 $\;$=$\;$ 3×1 $\;$+$\;$ 0×$\frac{1}{10}$ $\;$+$\;$ 9×$\frac{1}{100}$ $\;$=$\;$ 3 + $\frac{0}{10}$ + $\frac{9}{100}$ $\;$=$\;$ 3.09

We can read these lines left-to-right or right-to-left.

Interpreting 3.09 $\;$=$\;$ 3 × 1 $\;$+$\;$ 0 × $\frac{1}{10}$ $\;$+$\;$ 9 × $\frac{1}{100}$ from right-to-left is what she's being asked to do.

?

 

[JeffM]

This is just a different version of Dr. Peterson’s answer

$$6 * 1 + 5 * \dfrac{1}{10} = 6 + \dfrac{5}{1} * \dfrac{1}{10} = 6 + \dfrac{5}{10} = 6 + 0.5 = 6.5.$$
That is it. You need to know three things.

(1) If a is ANY number, then

$$a = \dfrac{a}{1}.$$
(2) If p, q, r, and s are numbers, and neither q nor s are zero, then

$$\dfrac{p}{q} * \dfrac{r}{s} = \dfrac{p * r}{q * s}.$$
(3) If d is a DIGIT,

$$\dfrac{d}{10} = 0.d, \ \dfrac{d}{100} = 0.0d, \ \dfrac{d}{1000} = 0.00d, \text { and so on.}$$