Lesson 1: Fractions and Decimals

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

A decimal number can be expressed in various equivalent forms, such as a mixed number or an improper fraction, by relating it to tenths and hundredths. Adding a trailing zero to a decimal renames it in smaller units without changing its value.

Examples

Property

A decimal's value does not change when a zero is added to the rightmost decimal place. Any number of tenths is equivalent to ten times that number of hundredths.

Examples