Decimals - Place Value in Decimals

Definition of Decimals: A decimal number is a way of expressing fractions using a decimal point to separate the whole number part from the fractional part. Imagine a single whole unit (like a square) being divided into 10 or 100 equal pieces; these pieces represent the decimal parts.

The Decimal Point: This is a small dot placed between the ones place and the tenths place. It acts as a separator. For example, in the number $12.35$, the dot tells us that $12$ is the whole part and $0.35$ is the part that is less than one.

Tenths Place ($\frac{1}{10}$): This is the first position to the right of the decimal point. If you visualize a long rectangle divided into $10$ equal vertical bars, one bar represents $1$ tenth or $0.1$. Ten tenths make one whole.

Hundredths Place ($\frac{1}{100}$): This is the second position to the right of the decimal point. If you visualize a large square grid divided into $100$ small squares (like a $10 \times 10$ graph), one tiny square represents $1$ hundredth or $0.01$. It takes $10$ hundredths to make $1$ tenth.

Thousandths Place ($\frac{1}{1000}$): This is the third position to the right of the decimal point. Visually, if you take one of the tiny hundredth squares and divide it further into $10$ thin strips, each strip is $1$ thousandth or $0.001$.

Place Value Relationship: As you move from left to right in a decimal number, the value of each place becomes $10$ times smaller. Conversely, moving from right to left, each place is $10$ times larger. For example, $0.1$ is $10$ times larger than $0.01$.

Expanded Form: Writing a decimal as the sum of the values of its individual digits. For example, the number $5.62$ can be visualized as $5$ whole blocks, $6$ tenth-strips, and $2$ hundredth-squares, written as $5 + \frac{6}{10} + \frac{2}{100}$.

Equivalent Decimals: Adding zeros to the extreme right of a decimal number does not change its value. For example, $0.4$, $0.40$, and $0.400$ all represent the same amount (four tenths). Visually, $4$ tenths strips occupy the same area as $40$ hundredths squares.