Help Translate expanded notation into standard form a00 + b0 + c =
- Thread starter madmath
- Start date
mmm4444bot
Super Moderator
- Joined
- Oct 6, 2005
- Messages
- 10,962
Hi mom.
It seems like the symbols a, b, and c each represent a digit in a three-digit number (i.e., each symbol stands for some arbitrary, whole number from 0 through 9 -- except that a is probably not 0 because there is no reason to add 000 to anything).
For example, a could represent the digit 4, and b could represent the digit 5, and c could represent the digit 6. Then we would have:
400 + 50 + 6 = 456
456 is standard form for the number four hundred fifty-six.
400 + 50 + 6 is an expanded form for the same number.
If we don't have values for a, b, and c, then we simply use these symbols as though they were the digits in a three-digit number.
In this case, the answer would be symbolic, representing standard form for any three-digit number:
a00 + b0 + c = abc.
The point of it all, I suppose, is to show a pattern, how three-digit numbers (like 456 or 274) can always be written as a sum of some hundreds plus some tens plus some ones:
4×100 + 5×10 + 6×1 = 400 + 50 + 6 = 456
2×100 + 7×10 + 4×1 = 200 + 70 + 4 = 274
In the three-digit number 274, the digit 2 is in the hundreds' position, the digit 7 is in the tens' position, and the digit 4 is in the ones' position.
In the symbolic number abc, we may think of a as representing the hundreds' position, b as representing the tens' position, and c as representing the ones' position.
A simple pattern that needs to be understood before studying math beyond arithmetic. Cheers :cool:
It seems like the symbols a, b, and c each represent a digit in a three-digit number (i.e., each symbol stands for some arbitrary, whole number from 0 through 9 -- except that a is probably not 0 because there is no reason to add 000 to anything).
For example, a could represent the digit 4, and b could represent the digit 5, and c could represent the digit 6. Then we would have:
400 + 50 + 6 = 456
456 is standard form for the number four hundred fifty-six.
400 + 50 + 6 is an expanded form for the same number.
If we don't have values for a, b, and c, then we simply use these symbols as though they were the digits in a three-digit number.
In this case, the answer would be symbolic, representing standard form for any three-digit number:
a00 + b0 + c = abc.
The point of it all, I suppose, is to show a pattern, how three-digit numbers (like 456 or 274) can always be written as a sum of some hundreds plus some tens plus some ones:
4×100 + 5×10 + 6×1 = 400 + 50 + 6 = 456
2×100 + 7×10 + 4×1 = 200 + 70 + 4 = 274
In the three-digit number 274, the digit 2 is in the hundreds' position, the digit 7 is in the tens' position, and the digit 4 is in the ones' position.
In the symbolic number abc, we may think of a as representing the hundreds' position, b as representing the tens' position, and c as representing the ones' position.
A simple pattern that needs to be understood before studying math beyond arithmetic. Cheers :cool:
Thanks: The entire question with multiple choice options
I am trying to help my fourth grader study for the Michigan Meap Assessment exam a state-wide assessment. I want her to do well.
I found a link online of previous exams given and this question was in the online booklet.
Goal to understand place value
Translate expanded notation into standard form a00 + b0 + c =
(incorrect) A a00 + b0 + c = a00,b0c
(incorrect) B a00 + b0 + c = a,b0c
(incorrect) C a00 + b0 + c = a,0bc
(answer D
not provided)
I am trying to help my fourth grader study for the Michigan Meap Assessment exam a state-wide assessment. I want her to do well.
I found a link online of previous exams given and this question was in the online booklet.
Goal to understand place value
Translate expanded notation into standard form a00 + b0 + c =
(incorrect) A a00 + b0 + c = a00,b0c
(incorrect) B a00 + b0 + c = a,b0c
(incorrect) C a00 + b0 + c = a,0bc
(answer D
not provided)
Great now i get it!!!
Great now I understand
a00 + b0 + c = abc
Explanation
a is in the hundredth place in a00 + b is in the tenth places + c in the ones place.
In a00 the zeros are representing place value for (a), in b0 the zeros are representing a place and the c is in the ones position
So the answer is>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
a00 + b0 + c = abc (correct answer)
OR VIEWED ANOTHER WAY>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
a00(hundreds)
b0 (tens)
+ c (ones
___________
abc (correct answer)
using your example of
Great now I understand
a00 + b0 + c = abc
Explanation
a is in the hundredth place in a00 + b is in the tenth places + c in the ones place.
In a00 the zeros are representing place value for (a), in b0 the zeros are representing a place and the c is in the ones position
So the answer is>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
a00 + b0 + c = abc (correct answer)
OR VIEWED ANOTHER WAY>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
a00(hundreds)
b0 (tens)
+ c (ones
___________
abc (correct answer)
using your example of