Decimal place value identifies the value of each digit in a decimal number by its position relative to the decimal point: ones, tenths, hundredths, and thousandths, with each place representing one-tenth the value of the place to its left. This includes interpreting standard, expanded, and fraction forms and understanding that zeros may hold a place without changing value; the scope does not extend to more distant decimal places or generalized powers-of-ten notation.
Detailed Explanation: Identify decimal place values
Start at the decimal point and read the places from left to right:
ones.tenths hundredths thousandths
Each place to the right is one-tenth the value of the place before it.
Example: Identify the place value and value of each digit in (5.204).
The 5 is to the left of the decimal point, so it is in the ones place. Its value is 5.
The 2 is the first digit to the right of the decimal point, so it is in the tenths place. Its value is 2 tenths, or 102​.
The 0 is the second digit to the right, so it is in the hundredths place. Its value is 0 hundredths, or 1000​. The zero holds the place so the other digits stay in the correct positions.
The 4 is the third digit to the right, so it is in the thousandths place. Its value is 4 thousandths, or 10004​.
The number can be written in expanded form as
5+102​+1000​+10004​.
So, in (5.204), the digits represent 5 ones, 2 tenths, 0 hundredths, and 4 thousandths.
Learn by doing: Identify decimal place values
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