Lesson 1: Understanding Tenths and Hundredths

Property

A tenth is one part of a whole that is divided into 10 equal parts. A hundredth is one part of a whole divided into 100 equal parts. We can write them as decimals:

Examples

• A whole is divided into 10 equal parts. If 3 parts are shaded, the decimal is 0.3.
• A whole is divided into 10 equal parts. If 7 parts are shaded, the decimal is 0.7.
• A whole is divided into 100 equal parts. If 45 parts are shaded, the decimal is 0.45.
• A whole is divided into 100 equal parts. If 12 parts are shaded, the decimal is 0.12.

Explanation

Tenths and hundredths represent parts of a whole using decimal notation. The position of a digit to the right of the decimal point shows how the whole is divided — into 10 equal parts for tenths and 100 equal parts for hundredths. The digits in these places describe how many parts of the whole are being represented, allowing us to express and understand amounts that are less than one whole.

Property

Decimals can have different numbers of digits but still represent the same value. For example:

• 0.3 represents 3 parts out of 10 equal parts of a whole.
• 0.30 represents 30 parts out of 100 equal parts of the same whole.

Even though the two decimals have a different number of digits, they represent the same amount.