Decimals - Place Value in Decimals

Understanding Decimals: A decimal number consists of a whole number part and a fractional part separated by a dot called the decimal point. For example, in $12.5$, $12$ is the whole number and $.5$ represents the part of a whole.

The Tenths Place: When one whole is divided into $10$ equal parts, each part is called one-tenth. Visually, imagine a rectangular bar divided into $10$ equal vertical strips; shading one strip represents $\frac{1}{10}$ or $0.1$. It is the first digit to the right of the decimal point.

The Hundredths Place: When one whole is divided into $100$ equal parts, each part is called one-hundredth. Visually, imagine a large square grid made of $10$ rows and $10$ columns (total $100$ small squares); shading one tiny square represents $\frac{1}{100}$ or $0.01$. It is the second digit to the right of the decimal point.

Place Value Chart: To the left of the decimal point, we have Ones, Tens, and Hundreds. To the right, we have Tenths ($\frac{1}{10}$) and Hundredths ($\frac{1}{100}$). Moving one place to the right divides the value by $10$, while moving one place to the left multiplies it by $10$.

Reading Decimals: We read the whole number part normally, say 'point' for the decimal, and then read each digit to the right individually. For example, $4.75$ is read as 'Four point seven five' or 'Four and seventy-five hundredths'.

Expanded Form: Decimals can be broken down into the sum of the values of their digits. For example, $6.34$ is written as $6 + \frac{3}{10} + \frac{4}{100}$ or $6 + 0.3 + 0.04$.

Equivalent Decimals: Adding zeros to the right of the last digit in a decimal does not change its value. For instance, $0.5$ is the same as $0.50$, which can be visualized as $5$ tenths of a bar being the same area as $50$ hundredths of the same bar.