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Question 695032: i am a three digit number . i am the largest number you can write with 6 in the hundredths place.
I dont get it , help please
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! We can analyze any math problem by looking at everything we are dealing with. In this problem, we are dealing with two things. The two things are both properties of a certain number. The first says that the number is three digits. This part is pretty easy. The number is anywhere from 100 to 999 by this information. The reason it is not 99 is because that is a two-digit number, and the reason that it cannot be 1000 is because that is a four-digit number. Any number between 100 and 999 are three digits. The second part can be tricky because the way it is worded. Let us analyze this property.
"I am the largest number you can write with 6 in the hundredths place." I am assuming that the word should be "hundreds", not "hundredths". "Hundredths" usually refers to the decimal place next to "tenths" and "thousandths". This place is found to the right of the decimal. The hundreds' place is found the left of the decimal. In any three-digit number, the hundreds' place is the first number that appears from left to right, or the far left number. If we have a number 501, the digit 5 is in the hundreds' place. (The structure of a three-digit number can be shown as hundreds-tens-ones.) This property says the number must have a 6 in the hundreds' place. We get this by "...you can write with 6 in the hundredths place." So, since our first property says the number must be a three-digit number and this property says that the number has a 6 in the hundreds' place, we can begin writing our number as so:
6 _ _.
The final piece of information in the second property tells us our number. It says that this number is the LARGEST number that can be written with a 6 in the hundreds' place. That is, with 6 in the hundreds' place, the number after this number would change the hundreds' place to a 7. We know from basic counting that as we go from one place to another (ones to tens, tens to hundreds, and so forth), the 9 changes to a 0 but the next number place goes up by 1. For example, if we have 9 and want to go to the next number, we would have 10. The 9 in the ones place in the first number "resets" to 0, but the place next to it (on the left), or the tens' place, goes up by 1. If we had 249, the next number would be 250 (9 goes to 0 and the 4 goes to 5). If we take this same logic, we can pinpoint our number with great accuracy.
We can look at it like this: Since the hundreds' place MUST be 6, what is the largest three-digit number that has 6 in its hundreds' place? Or, if we go up by just one more number, the hundreds' place would change into 7 because we can't get any higher with 6 in the hundreds' place. (This number must be the largest 6-in-the-hundreds'-place number that can be written.) This number is
6 _ _
6 9 9
699.
If we look at this number, if we try going up by just one, the ones' place would reset to 0 because we have a 9 in that place. Therefore, the next place would go up by 1, or the tens' place would go up by 1. But since this number is also 9, the tens' place resets to 0 and the next number rises by 1. This number is 6 to begin with, but now it would become 7. We can't have that because there must be a 6 in the hundreds' place, not a 7. That is why 699 is the "largest number you can write with 6 in the hundredths place." If we try having a larger number, the hundreds' place changes. 699 is a three-digit number also, so it meets the requirements.
You must remember that both properties are for the same number. Both sentences describe this same number.
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