Key Points

To measure quantities with greater accuracy, we divide a whole unit into smaller, equal parts. This is necessary when measurements are not exact whole numbers, such as the length of a small screw.

When one whole unit is divided into 10 equal parts, each part is called a 'tenth' (1/10). This is the first place value to the right of the decimal point.

For even more precision, each tenth is divided into 10 more parts, resulting in 100 parts in a whole unit. Each of these parts is a 'hundredth' (1/100).

The place value system extends to the right of the ones place for fractional parts. The places are tenths, hundredths, thousandths, and so on, with each place being 10 times smaller than the one to its left.

A decimal point ('.') is used to separate the whole number part of a number from its fractional part. Digits to the left of the point are whole numbers, and digits to the right represent parts of a whole.

To read a decimal, read the whole number part, say 'point', and then read the digits of the fractional part individually. For example, 7.05 is read as 'seven point zero five'.

Decimals are used to convert between metric units. For example, since 1 cm = 10 mm, 1 mm is equal to 0.1 cm. Similarly, 1 cm is equal to 0.01 m.

The decimal system is also used for weight and money conversions. For instance, 1 gram is 0.001 kilograms, and 1 paisa is 0.01 rupees.

Decimals can be precisely located on a number line by dividing the segment between two whole numbers into 10 equal parts for tenths, and further subdividing for hundredths.

To compare decimals, start from the leftmost digit and compare digits in the same place value. The number with the larger digit at the first point of difference is the greater number.

Adding zeros to the right end of a decimal number does not change its value. For example, 0.2, 0.20, and 0.200 all represent the same quantity, which is two-tenths.

To add or subtract decimals, align the numbers vertically so that the decimal points line up. Then, perform the operation as you would with whole numbers, placing the decimal point in the answer directly below the others.

Correct placement of the decimal point is critical in real-world applications like finance, medicine, and engineering. A small error can lead to significant problems.