Tenth — Definition, Formula & Examples

A tenth is one of ten equal parts of a whole. You can write it as the fraction

\frac{1}{10}

or as the decimal

0.1

A tenth represents a single unit when a whole is partitioned into ten parts of equal size. In decimal notation, the tenths place is the first digit to the right of the decimal point, indicating how many groups of $\frac{1}{10}$ are present.

How It Works

Picture a pizza cut into 10 equal slices. Each slice is one tenth of the pizza. If you eat 3 slices, you have eaten

\frac{3}{10}

of the pizza, which equals

0.3

. In a decimal number like

4.7

, the digit 7 sits in the tenths place, meaning there are 7 tenths in addition to the 4 wholes.

Worked Example

Problem: A ribbon is 10 inches long. You cut it into 10 equal pieces. How long is each piece as a fraction and as a decimal?

Step 1: Divide the whole length into 10 equal parts.

\frac{10}{10} = 1 \text{ inch per piece}

Step 2: Each piece is one tenth of the full ribbon.

\frac{1}{10} = 0.1

Answer: Each piece is

\frac{1}{10}

of the ribbon, or

0.1

of the whole (which here equals 1 inch).

Why It Matters

Tenths are the bridge between fractions and decimals. Understanding them helps you read measurements, work with money (a dime is one tenth of a dollar), and build the place-value skills needed for adding and comparing decimals.

Common Mistakes

Mistake: Confusing the tenths place with the tens place.

Correction: The tens place is to the left of the ones digit (like the 3 in 30). The tenths place is the first digit to the right of the decimal point (like the 3 in 0.3). One is ten times bigger, the other is ten times smaller than one.