Decimals - Using Decimals in Money, Length, and Weight

Expressing Money using Decimals: Since $100$ paise make $1$ rupee, we can say $1$ paisa is one-hundredth of a rupee. To convert paise to rupees, we divide by $100$, resulting in two decimal places. For example, $5$ paise is written as $₹ \frac{5}{100} = ₹ 0.05$. Visually, imagine a $10 \times 10$ grid representing $1$ rupee; shading $5$ small squares represents $0.05$ rupees.

Length in Centimeters and Millimeters: There are $10$ millimeters in $1$ centimeter. Therefore, $1$ mm is one-tenth of a cm, or $0.1$ cm. On a standard ruler, the small marks between $0$ and $1$ represent $0.1$ cm each. If an object is $2$ cm and $3$ mm long, it is written as $2.3$ cm.

Length in Meters and Centimeters: Since $100$ cm equals $1$ m, $1$ cm is $0.01$ m. When expressing lengths like $155$ cm in meters, we divide by $100$ to get $1.55$ m. Visualize a meter rod as a whole unit divided into $100$ equal parts, where each part is $0.01$ m.

Distance in Kilometers and Meters: Large distances are measured in kilometers, where $1000$ m = $1$ km. This means $1$ m = $\frac{1}{1000}$ km = $0.001$ km. To convert meters to kilometers, we move the decimal point three places to the left. For instance, $45$ m becomes $0.045$ km.

Weight in Kilograms and Grams: Weight follows a similar decimal pattern where $1000$ g = $1$ kg. Thus, $1$ g = $0.001$ kg. If you see a digital scale showing $2$ kg and $500$ g, it can be represented as $2.500$ kg. The three digits after the decimal represent the grams.

Unit Conversion Rule: To convert from a smaller unit to a larger unit (like g to kg or cm to m), we divide by the conversion factor ($10$, $100$, or $1000$). The number of zeros in the divisor tells us how many places the decimal point moves to the left from the end of the number.

Decimal Place Value in Measures: In measurements, the digits after the decimal point represent the fractional parts of the higher unit. In $5.75$ m, '$5$' is the whole meters, '$7$' is tenths of a meter ($70$ cm), and '$5$' is hundredths of a meter ($5$ cm).