Fractions (Including Problems)
Decimal Fractions (Decimals)
Exponents (Including Laws of Exponents)
Ratio and Proportion (Including Sharing in a Ratio)
Unitary Method (Including Time and Work)
Percent and Percentage
Profit, Loss and Discount
Fundamental Concepts (Including Fundamental Operations)
Simple Linear Equations (Including Word Problems)
Set Concepts (Some Simple Divisions by Vedic Method)
Lines and Angles (Including Construction of Angles)
Symmetry (Including Reflection and Rotation)
Recognition of Solids (Representing 3-d in 2-d)
Congruency: Congruent Triangles
Data Handling (Statistics)
Decimal Representation of Rational Numbers:
1) Write the rational number `7/4` in decimal form.
(1) 7 = 7.0 = 7.000 (Any number of zeros can be added after the fractional part.)
(2) 1 is the quotient and 3 the remainder after dividing 7 by 4. Now we place a decimal point after the integer 1. Writing the 0 from the dividend after the remainder 3, we divide 30 by 4. As the quotient, we get now is fractional, we write 7 after the decimal point. Again we bring down the next 0 from the dividend and complete the division.
2) Write `2 1/5` in decimal form.
We shall find the decimal form of `2 1/5 = 11/5` in three different ways.
Find the decimal form of `1/5`.
∴ `1/5` = 0.2
3) Write the number `2/11` in decimal form.
∴ `2/11` = 0.1818.......
`2/11 = 0.bar18`
4) Work out the decimal form of `5/6`.
`5/6` = 0.833...
`∴ 5/6 = 0.8dot3`
Here, a single digit or a group of digits occurs repeatedly on the right of the decimal point. This type of decimal form of a rational number is called the recurring decimal form.
If in a decimal fraction, a single-digit occurs repeatedly on the right of the decimal the point, we put a point above it as shown here. `5/6 = 0.8dot3` and if a group of digits occurs repeatedly, we show it with a horizontal line above the digits. Thus, `2/11 = 0.bar18`.