The 1-to-10 Relationship Between Places
The 1-to-10 Relationship Between Places is a Grade 4 math skill in enVision Mathematics, Chapter 1: Generalize Place Value Understanding. Students learn that each place in our number system is exactly 10 times greater than the place to its right, forming the foundation of base-ten understanding.
Key Concepts
Property The value of a digit in a given place is equal to the value of the same digit in the place to its immediate left divided by 10. $$\text{Value of a digit} = \text{Value of the digit to the left} \div 10$$.
Examples In the number 770, the value of the 7 in the tens place (70) is the value of the 7 in the hundreds place (700) divided by 10. So, $70 = 700 \div 10$. In the number 2,245, the value of the 2 in the hundreds place (200) is the value of the 2 in the thousands place (2000) divided by 10. So, $200 = 2000 \div 10$.
Explanation This property explains the relationship between adjacent place values as you move from left to right. Each time you move one place to the right, the value of the digit becomes ten times smaller. This is the same as dividing the value of the digit by 10. Understanding this division relationship is key to comparing the value of digits within a number.
Common Questions
What is the 1-to-10 relationship between place values?
Each place in the base-ten number system is exactly 10 times the value of the place to its right. So tens are 10 times ones, hundreds are 10 times tens, and so on.
How does the 1-to-10 relationship help with multiplication?
Understanding that each place is 10 times greater helps explain why multiplying by 10 shifts all digits one place to the left, making mental multiplication with multiples of 10 easier.
What is an example of the 1-to-10 relationship?
If you have 4 in the tens place, it represents 4 times 10 equals 40. If that same 4 moved to the hundreds place, it would represent 4 times 100 equals 400, which is 10 times greater.
How does the 1-to-10 relationship help with division?
Understanding this relationship helps explain why dividing by 10 shifts digits one place to the right, reducing the value by a factor of 10.
What chapter covers place value relationships in enVision Grade 4?
The 1-to-10 relationship between places is covered in Chapter 1: Generalize Place Value Understanding in enVision Mathematics Grade 4.