Tenths and Hundredths - Measurement of Length and Money in Decimals

Tenths represent one part out of ten equal divisions of a whole. In decimal notation, one-tenth is written as $0.1$. Visually, imagine a $1 \text{ cm}$ segment on a ruler divided into $10$ equal small divisions; each division represents $1 \text{ mm}$ or $0.1 \text{ cm}$.

Hundredths represent one part out of a hundred equal divisions of a whole, written as $0.01$. Visually, if you look at a square grid consisting of $100$ small squares, shading exactly one square represents $0.01$ (one-hundredth) of the entire grid.

When measuring length, we often use the relationship between millimeters and centimeters. Since $10 \text{ mm} = 1 \text{ cm}$, a single millimeter is $\frac{1}{10}$ of a centimeter. Therefore, a measurement like $3 \text{ mm}$ is written as $0.3 \text{ cm}$.

For larger length measurements, we convert centimeters to meters. Because $100 \text{ cm} = 1 \text{ m}$, $1 \text{ cm}$ is $\frac{1}{100}$ of a meter, written as $0.01 \text{ m}$. Visually, if a ribbon is $150 \text{ cm}$ long, it is $1$ whole meter and $50$ hundredths of a meter, or $1.50 \text{ m}$.

Money in India is calculated using Rupees and Paise. Since $100 \text{ Paise} = ₹ 1$, one Paisa is one-hundredth of a Rupee. We use a decimal point to separate Rupees from Paise; for example, $75 \text{ Paise}$ is written as $₹ 0.75$.

The Decimal Place Value Chart helps organize these parts. The first position to the right of the decimal point is the 'Tenths' place, and the second position to the right is the 'Hundredths' place. For example, in $4.56$, $5$ is the number of tenths and $6$ is the number of hundredths.