Place Value
Place value is a foundational Grade 5 math concept in enVision Mathematics, Chapter 1: Understand Place Value. Each position in a number represents a value 10 times greater than the position to its right, so a number like 3,041 equals 3×1000 + 0×100 + 4×10 + 1. Understanding place value is essential for all arithmetic operations with whole numbers and decimals.
Key Concepts
Property Each place represents 10 times the place just to the right. A number is a sequence of digits, and its value is the sum of each digit multiplied by its place value (a power of ten). For example: $$3041 = 3 \times 1000 + 0 \times 100 + 4 \times 10 + 1$$ This can also be written using exponents: $$3041 = 3 \times 10^3 + 0 \times 10^2 + 4 \times 10^1 + 1 \times 10^0$$.
Examples The number 5,281 in expanded form is $5 \times 1000 + 2 \times 100 + 8 \times 10 + 1$. The number 709 shows the importance of zero as a placeholder. It is $7 \times 100 + 0 \times 10 + 9$. A larger number like 1,607,300 is written as $1 \times 1000000 + 6 \times 100000 + 0 \times 10000 + 7 \times 1000 + 3 \times 100 + 0 \times 10 + 0 \times 1$.
Explanation Place value is like a secret code where a digit's position tells you its real worth. A 7 in the tens place is 70, but in the hundreds place, it's 700! This system lets us write any number, big or small.
Common Questions
What is place value?
Place value is the value of a digit based on its position in a number. Each place is 10 times the value of the place to its right, so the hundreds place is worth 100, the tens worth 10, and so on.
What is the place value of 4 in 3,041?
The 4 is in the tens place, so its value is 4 × 10 = 40.
How does place value help with addition and subtraction?
It allows you to line up digits by their value and operate on matching places separately, making calculations systematic and accurate.
Where is place value taught in enVision Grade 5?
Chapter 1: Understand Place Value in enVision Mathematics, Grade 5.
How is place value used with decimals?
Decimals extend place value to the right of the decimal point: tenths, hundredths, thousandths. The same rule applies—each place is 1/10 the value of the place to its left.