Chapter 8: Decimals (Notes)
Posted on : 19-11-2017 Posted by : Admin

What are Decimal numbers?

• Decimals are used in many ways in our lives. For example, for representing units of money, length and weight.
• Decimals represent the part of the whole number.
• Numbers written in decimal form are caled decimal numbers or decimals.
• A decimal has two parts-Whole number part or the integral part and decimal part.

Consider the decimal number, 378.492

378.492

Note that the numbers to the left of the decimal point is called the whole number part and it is read as three hundred seventy eight while the numbers on to the right of the decimal point is called decimal part and it is read as Four Nine Two.

Hence this decimal number is read as three hundred seventy eight point four nine two. 

What are Decimal fractions?

The fractions in which the denominators are 10, 100 and 1000, etc. are called as Decimal fractions.

For example:

$\frac{8}{10}, \frac{29}{100}, \frac{81}{1000},\frac{62}{10000}$

• We use dot to write the decimal numbers and this dot is called as the decimal point. When a whole number is divided into 10 equal pats, then each part is called one-tenth of a unit. This can be ritten as $\frac{1}{10}$ and 0.1 in decimal notations.
• When a whole number is divided into 10 equal parts, then each part is called one-tenth of a unit. This can be written as $\frac{1}{10}$ and 0.1 in decimal notations.
• Similarly, when a whole number is divided into 100 equal parts, then each part is called one-hundredth of a unit and written as $\frac{1}{100}$ and 0.01 in decimal notation.

Place values of Decimal numbers

• The positions to the right of the decimal point are called as the decimal places.
• Each decimal degit occupies a decimal place.
• In standard form, the decimal is always put between the unit place and tenths-place.
• In the place value chart, as we go from left to the right, the multiplying factor becomes factor $\frac{1}{10}$ of the previous factor.
• All decimals can be represented on number line.

Like Decimals and Unlike Decimals

Decimal numbers having the same number of decimal places are called ‘Like decimals’.
For example: 0.89, 1.62, 3.88 are all like decimals.

Decimal numbers having different number of decimal places are called ‘unlike decimals’.
For example: 2.96, 4.065, 9.12356 are all unlike decimals.