Lesson 34: Decimal Place Value

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.

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.

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.

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.

Property

We use a decimal point to mark the separation between the ones place and places with values less than one.

Examples

• In the number $42,876.39$, the decimal point separates the whole number part ($42,876$) from the fractional part ($0.39$).
• The number $5.4321$ has a decimal point that shows '5' is the whole number and '.4321' represents the part that is less than one.
• In $0.0123$, the decimal point shows there are no whole numbers, only the fractional amount to its right.

Explanation

Think of the decimal point as the official gatekeeper of numbers! It stands right after the ones place, separating the whole numbers on the left from the tiny, fractional parts on the right. Everything to its left is a whole value, while everything to its right is a piece of a whole, getting smaller and smaller.

Property

Thinking about money is a helpful way to remember decimal place values. A mill is $\frac{1}{1000}$ of a dollar and $\frac{1}{10}$ of a cent.

Examples

• One hundredth of a dollar is a cent, which can be written as $0.01$ dollars.
• One thousandth of a dollar is a mill, which is used in gasoline prices like $2.299$ dollars per gallon.
• A dime is one tenth of a dollar, which we can write as $0.1$ dollars, showing its value in the tenths place.

Explanation

If decimals feel weird, just think about your wallet! A dollar is your 'one.' Dimes are tenths ($0.10$ dollars), and pennies are hundredths ($0.01$ dollars). Even gas prices use thousandths with that extra little nine at the end. Using money as a guide is a real-world cheat sheet that makes decimal places make 'cents'!