Decimal Place Value
Decimal place value extends the base-ten number system to the right of the decimal point, with each position representing a fraction: tenths (1/10), hundredths (1/100), thousandths (1/1000). In Grade 6 Saxon Math Course 1 (Chapter 4: Number, Operations, and Measurement), students name and write the value of each digit in a decimal number. In 34.56, the 3 is in tens, 4 in ones, 5 in tenths, and 6 in hundredths—so 5 represents 5/10 and 6 represents 6/100. The decimal point works like the word and when reading money: 12 dollars and 50 cents = 12.50. Understanding this positions students to compare, add, and multiply decimals accurately.
Key Concepts
New Concept A decimal point separates whole numbers from fractional parts. Each place to the right of the decimal point has a value one tenth of the place to its left. $$ \text{ones} \xrightarrow{\frac{1}{10} \text{ of 1 is } \frac{1}{10}} \text{tenths} \xrightarrow{\frac{1}{10} \text{ of } \frac{1}{10} \text{ is } \frac{1}{100}} \text{hundredths} \xrightarrow{\frac{1}{10} \text{ of } \frac{1}{100} \text{ is } \frac{1}{1000}} \text{thousandths} $$ What’s next This is just the foundation. Next, you'll analyze worked examples to identify digits in specific places and determine the place value of any digit.
Common Questions
What place value positions exist to the right of the decimal point?
From left to right: tenths (1/10), hundredths (1/100), thousandths (1/1000), ten-thousandths (1/10,000). Each is ten times smaller than the position to its left.
In 34.56, what is the value of the digit 5?
5 is in the tenths place. Its value is 5 × (1/10) = 5/10 = 0.5.
How do you read 12.50 in words?
Twelve and fifty hundredths, or twelve dollars and fifty cents in a money context.
What fraction is equivalent to the digit 7 in 0.07?
7 is in the hundredths place, so its value is 7/100.
How is decimal place value similar to whole number place value?
Both follow base-ten: each position is 10 times the value of the position to its right. Whole numbers use ones, tens, hundreds; decimals use tenths, hundredths, thousandths.