Session 4: Uses of Decimal Notation – Conversion Chart and Examples

Decimals have some broad and surprising applications in our everyday life. It is primarily used when precision is required, like finding out the exact weight on a scale. You might have seen decimals in a thermometer reading as well. This section deals with the applications of decimals in our day to day lives.

Money

One of the most common applications of decimals is for money. One rupee is made up of hundred paise. Often we also have to convert rupees into paise while shopping, to calculate the amount of the final product.

It takes 100 paise to make one rupee or one whole. One paisa is one out of a hundred. 

How can we write 5 paise as a decimal? To do this, we need to think about 5 out of 100. We can say that 5 paise is 5 hundredths of a rupee since there are 100 paise in one rupee.

Conversion between Paise and Rupee

100 paise = ₹ 1  So, 1 p=₹\(\frac{1}{100}\)=₹0.01

Examples:

i. 9 p = 9 hundredths of a rupee₹=\(\frac{9}{100}\)×₹1=₹0.09

ii. 17 p = 17 hundredths of a rupee=\(\frac{17}{100}\)×₹1=₹0.17

iii. 25 p = 25 hundredths of a rupee=₹0.25

iv. 6 rupees 37 paise=₹6+₹0.37=₹6.37

v. 392 rupees 6 paise=₹392+₹0.06=₹392.06

Decimal metric system

By the 18th century, dozens of different units of measurement were commonly used throughout the world. Length, for example, could be measured in feet, inches, miles, spans, cubits, hands, and more. The lack of common standards led to confusion and significant inefficiencies in trade between countries. At the end of the century, the French government devised a system of measurement that could be used throughout the world. This system is known as the metric system. 

The decimal metric system is a system of units in which the multiples and sub-multiples of the unit of measurement are interrelated by multiples or sub-multiples of 10. 

Measurements of Length: Conversion Chart

The base unit of length is the metre. However, there are other units:

Conversion between mm and cm

10 mm=1 cm So, 1 mm=\(\frac{1}{10}\)cm=0.1 cm

Examples:

Conversion between cm and m

100 cm=1 m So, 1 cm=\(\frac{1}{100}\) m=0.01 m

Examples: 

Conversion between m and km

1000 m=1 km So, 1 m=\(\frac{1}{1000}\) km=0.001 km

Examples:

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Measurements of Weight: Conversion Chart

The base unit of weight is the gram. However, there are other units:

Conversion between mg and g

1000 mg=1 g So, 1 mg=\(\frac{1}{1000}\) g=0.001 g

Examples:

Conversion between g and kg

1000 g=1 kgSo, 1 g=\(\frac{1}{1000}\) kg=0.001 kg

Examples:

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Measurements of Capacity: Conversion Chart

The base unit of capacity is the litre. However, there are other units: 

Conversion between mL and L

1000 ml=1 l So, 1 ml=\(\frac{1}{1000}\)l=0.001 l

Examples:

Conversion between L and kL

1000 l=1 kl So, 1 l=\(\frac{1}{1000}\) kl=0.001 kl

Examples:

Notice that the relationship between the units of measurement is all based on powers of 10. This is because the metric system is based on powers of 10, just like our number system. To move between different lengths, weights, and capacity units, all we need to do is move the decimal point.

• Any time we go from a smaller unit of measure to a larger unit of measure we will need to divide or move the decimal point to the left.
• Any time we are going from a larger unit of measure to a smaller unit of measure we will need to multiply or move the decimal point to the right.