BitWithBite
Arithmetic (Beginner) · Quick Reference
Place Value Cheat Sheet
In one line: place value tells us what a digit is worth based on its position in a number. The same digit can represent very different amounts depending on where it sits.
Key Ideas
1Place vs. Value. 'Place' is the position (ones, tens, hundreds...). 'Value' is what the digit is worth there (digit x place).
2Expanded Form. Writing a number as the sum of the value of each digit. Example: present present present present present present present present present present present present present present present present.
3Face Value. The digit itself, regardless of position (the face value of 7 in 375 is simply 7).
4Decimal Place Value. Positions after the decimal point are tenths, hundredths, thousandths, each getting smaller by a factor of 10.
Worked Examples
What is the place value of 5 in 3,542?
500
Write 4,067 in expanded form.
4000 + 0 + 60 + 7
In the number 12.34, what is the place value of the 3?
Tenths place, value = 3/10 = 0.3
Formulas
Value of a digit = digit x (10^position), counting the ones place as position 0.
Practice Yourself
What is the place value of 8 in 812?
Hundreds (800)
What is the face value of 8 in 812?
8
Write 250 in expanded form.
200 + 50 + 0