Tenths and Hundredths - Conversion between Fractions and Decimals

Understanding Tenths: When a whole object or group is divided into 10 equal parts, each part is called one-tenth. In fraction form, it is written as $\frac{1}{10}$ and in decimal form as $0.1$. Visually, imagine a long chocolate bar divided into 10 equal vertical slices; eating one slice means you ate $0.1$ of the bar.

Understanding Hundredths: When a whole is divided into 100 equal parts, each part is one-hundredth. This is written as $\frac{1}{100}$ or $0.01$. If you look at a large square grid containing 100 small squares ($10 \times 10$), shading just one tiny square represents $0.01$ of the whole grid.

The Decimal Point: The decimal point is a dot used to separate the whole number part from the fractional part. For example, in $15.36$, $15$ is the whole number, and $0.36$ represents $3$ tenths and $6$ hundredths.

Converting Tenths to Decimals: To convert a fraction with a denominator of $10$ to a decimal, we write the numerator and place the decimal point one digit from the right. For example, $\frac{5}{10} = 0.5$. If the fraction is $\frac{12}{10}$, it becomes $1.2$.

Converting Hundredths to Decimals: To convert a fraction with a denominator of $100$, we place the decimal point two digits from the right. For example, $\frac{25}{100} = 0.25$. If the numerator has only one digit, like $\frac{7}{100}$, we add a zero to the left of the digit to keep the place value, resulting in $0.07$.

Place Value Chart: Decimals follow a specific place value system. To the left of the decimal are Ones, Tens, and Hundreds. To the right are Tenths ($\frac{1}{10}$) and Hundredths ($\frac{1}{100}$). In the number $4.72$, the digit $7$ is in the tenths place and $2$ is in the hundredths place.

Equivalent Decimals: Adding zeros to the right of a decimal number does not change its value. For instance, $0.5$ is equal to $0.50$. Visually, shading $5$ out of $10$ columns in a grid is the exact same total area as shading $50$ out of $100$ small squares.

Money and Decimals: In the Indian currency system, $1$ Rupee = $100$ Paise. Therefore, $1$ Paisa = $\frac{1}{100}$ Rupee = $₹ 0.01$. This makes money a perfect real-world example of the hundredths place value.