Decimals - Tenths and Hundredths

Understanding Tenths: When a whole unit is divided into 10 equal parts, each part is called a tenth. In decimal notation, one-tenth is written as $0.1$ and as a fraction $\frac{1}{10}$. Visually, imagine a rectangle divided into 10 equal vertical columns; shading one column represents $0.1$.

Understanding Hundredths: When a whole unit is divided into 100 equal parts, each part is a hundredth. It is written as $0.01$ or $\frac{1}{100}$. Visually, this looks like a large $10 \times 10$ square grid where a single tiny square out of the 100 total squares is shaded.

Decimal Place Value Chart: The decimal point separates the whole number part from the fractional part. Moving to the right of the decimal point, the places are Tenths ($\frac{1}{10}$), then Hundredths ($\frac{1}{100}$). For example, in $5.28$, $5$ is in the ones place, $2$ is in the tenths place, and $8$ is in the hundredths place.

Decimals on a Number Line: To represent tenths on a number line, the distance between two consecutive whole numbers (like $0$ and $1$) is divided into 10 equal intervals. The third tick mark after $0$ represents $0.3$. For hundredths, each tenth interval is further divided into 10 tiny segments.

Converting Fractions to Decimals: Fractions with denominators of $10$ or $100$ can be written directly as decimals. If the denominator is $10$, there is one digit after the decimal point (e.g., $\frac{7}{10} = 0.7$). If the denominator is $100$, there are two digits after the decimal point (e.g., $\frac{9}{100} = 0.09$).

Comparing Decimals: To compare two decimals, first look at the whole number part. If they are equal, compare the digits in the tenths place. If those are also equal, compare the digits in the hundredths place. For instance, $0.5 > 0.05$ because $5$ tenths is greater than $0$ tenths.

Expanded Form: A decimal can be written as the sum of its digits multiplied by their place values. For example, $14.36$ can be visualized as $10 + 4 + \frac{3}{10} + \frac{6}{100}$, showing how many tens, ones, tenths, and hundredths make up the number.