A Peek Beyond the Point - More on the Decimal System

The decimal system extends the place value system to represent parts of a whole using a decimal point. The places to the right of the decimal point are Tenths ($\frac{1}{10}$), Hundredths ($\frac{1}{100}$), and Thousandths ($\frac{1}{1000}$).

To compare two decimal numbers, first compare the whole number parts. If they are equal, compare the tenths digit. If those are also equal, compare the hundredths digit, and so on.

Decimals are used to convert units: $1 \text{ paisa} = ₹ \frac{1}{100} = ₹ 0.01$, $1 \text{ g} = \frac{1}{1000} \text{ kg} = 0.001 \text{ kg}$, and $1 \text{ cm} = \frac{1}{100} \text{ m} = 0.01 \text{ m}$.

When multiplying a decimal by $10, 100, \text{ or } 1000$, the decimal point shifts to the right by as many places as there are zeros.

When dividing a decimal by $10, 100, \text{ or } 1000$, the decimal point shifts to the left by as many places as there are zeros.

To multiply two decimals, multiply them as if they were whole numbers. The number of decimal places in the product is the sum of the decimal places in the two factors.

To divide a decimal by another decimal, multiply both the dividend and the divisor by a power of $10$ (like $10, 100, 1000$) to make the divisor a whole number, then divide.