Decimal Place Value
Decimal place value describes how every position to the right of the decimal point is exactly one-tenth the value of the position to its left. In Grade 6 Saxon Math Course 1, students learn that the first decimal place is tenths (1/10), the second is hundredths (1/100), and the third is thousandths (1/1000). In the number 3.741, the digit 7 has value 7 tenths, 4 has value 4 hundredths, and 1 has value 1 thousandth. Mastering decimal place value is prerequisite to comparing, ordering, and computing with any decimal number.
Key Concepts
Property Each place to the right of the ones place has a value one tenth the value of the place to its left. Places to the right of a decimal point are often called decimal places. $$ ext{ones} \xrightarrow{\frac{1}{10} \text{ of 1 is } \frac{1}{10}} \text{tenths} \xrightarrow{\frac{1}{10} \text{ of } \frac{1}{10} \text{ is } \frac{1}{100}} \text{hundredths} \xrightarrow{\frac{1}{10} \text{ of } \frac{1}{100} \text{ is } \frac{1}{1000}} \text{thousandths} $$.
Examples In the number $12.345$, the place value of the 5 is the thousandths place, three spots to the right of the decimal point. What is the place value of the 8 in $67.89$? The 8 is in the first spot to the right of the decimal, so it is the tenths place. In $5.4321$, the digit in the tenths place is 4, because it is the first digit immediately following the decimal point.
Explanation Imagine numbers live on a street with the 'ones' house at the center. Moving left, houses get 10 times bigger. But take a step right, past the decimal point fence, and they get 10 times smaller! You enter the land of tiny fractions where everything ends in ' ths,' like tenths, hundredths, and so on.
Common Questions
What are the first three decimal place values to the right of the decimal point?
Tenths (1/10), hundredths (1/100), thousandths (1/1000) — each one-tenth of the place to its left.
What is the value of the digit 4 in 2.047?
4 is in the hundredths place, so its value is 4/100 = 0.04.
How does decimal place value connect to money?
The tenths place represents dimes (10 cents) and the hundredths place represents pennies (1 cent), making place value very concrete for students.
Why does each decimal place get ten times smaller moving right?
Our base-10 number system means each place is worth one-tenth of the place to its left, whether left or right of the decimal point.
How do you read 5.306 by place value?
Five and three hundred six thousandths: 3 is in tenths, 0 in hundredths, 6 in thousandths.