In our number system, also known as the decimal system, numbers are written using 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit's value depends on its position within the number.
When we write a number in expanded form with base 10 notation, we break down the number into its individual place values. For example, the number 346 can be expanded as 300 + 40 + 6.
The reason why the expanded form with base 10 notation equals the number itself is because each digit position represents a power of 10. In the number 346, the digit 3 is in the hundreds place, the digit 4 is in the tens place, and the digit 6 is in the ones place.
So, when we evaluate the expanded form using base 10 notation, we can calculate the value of each digit by multiplying it with the corresponding power of 10 and then summing them up.
In this case, 3 x 100 + 4 x 10 + 6 x 1 equals 300 + 40 + 6, which is equal to 346. Thus, the expanded form with base 10 notation gives us the original number itself in our number system.
Explain in your own words:
Why are numbers in expanded form with base 10 notation equal to the number itself for our number system?
5 answers
can u explain in a simple way or how an 8th grader would write this
Sure, I can explain it in a simpler way for an 8th grader:
In our number system, we use digits from 0 to 9 to write numbers. Each digit's value depends on its position in the number. When we write a number in expanded form with base 10 notation, it means we break it down into its individual parts.
For example, let's take the number 346. To write it in expanded form with base 10 notation, we think about the value of each digit based on its position. The digit 3 is in the hundreds place, the digit 4 is in the tens place, and the digit 6 is in the ones place.
So, we can write it as 3 x 100 + 4 x 10 + 6 x 1. To find the value of each part, we multiply the digit in that place by the corresponding power of 10 and then add them up.
When we calculate 3 x 100 (which is 300), 4 x 10 (which is 40), and 6 x 1 (which is 6), and then add them together, we get the original number we started with, which is 346.
So, the expanded form with base 10 notation gives us the original number itself in our number system.
In our number system, we use digits from 0 to 9 to write numbers. Each digit's value depends on its position in the number. When we write a number in expanded form with base 10 notation, it means we break it down into its individual parts.
For example, let's take the number 346. To write it in expanded form with base 10 notation, we think about the value of each digit based on its position. The digit 3 is in the hundreds place, the digit 4 is in the tens place, and the digit 6 is in the ones place.
So, we can write it as 3 x 100 + 4 x 10 + 6 x 1. To find the value of each part, we multiply the digit in that place by the corresponding power of 10 and then add them up.
When we calculate 3 x 100 (which is 300), 4 x 10 (which is 40), and 6 x 1 (which is 6), and then add them together, we get the original number we started with, which is 346.
So, the expanded form with base 10 notation gives us the original number itself in our number system.
can u make this a full sentence but smaller
Sure! In our number system, when we write a number in expanded form with base 10 notation, it means we break down the number into its parts based on the value of each digit and its position. By adding these parts together, we get the original number.