The Concept of DecimalsExplain the concept of decimalsA decimal- is defined as a number which consist of two parts separated by a point.The parts are whole number part and fractional partExample 1
Example 2
Conversion of Fractions to Terminating Decimals and Vice VersaConvert fractions to terminating decimals and vice versaThe first place after the decimal point is called tenths.The second place after the decimal point is called hundredths e.t.cConsider the decimal number 8.152
NOTE
- To convert a fraction into decimal, divide the numerator by denominator
- To convert a decimal into fraction, write the digits after the decimal point as tenths, or hundredths or thousandths depending on the number of decimal places.
Example 3Convert the following fractions into decimals
SolutionDivide the numerator by denominator
Operations and DecimalsAddition of DecimalsAdd decimalsExample 4Evaluate
Solution
Subtraction of DecimalsSubtract decimalsExample 5
Solution
Multiplication of DecimalsMultiply decimalsExample 6
Solution
Mixed Operations with DecimalsPerform mixed operations with decimalsExample 7
Solution
Word Problems Involving DecimalsSolve word problems involving decimalsExample 8If 58 out of 100 students in a school are boys, then write a decimal for the part of the school that consists of boys.SolutionWe can write a fraction and a decimal for the part of the school that consists of boys.
| fraction | decimal |
| 58/100 | 0.58 |
PercentagesExpressing a Quantity as a PercentageExpress a quantity as a percentageThe percentage of a quantity is found by converting the percentage to a fraction or decimal and then multiply it by the quantity.Example 9
NOTE:The concept of percentage of a quantity can be used to solve the problems involving percentage increase and decrease as shown in the below examples:-A Fractions into Percentage and Vice VersaConvert a fraction into percentage and vice versaTo change a fraction or a decimal into a percentage, multiply it by 100%Example 10Convert the following fractions into percentages
A Decimal into Percentage and Vice VersaConvert a decimal into percentage and vice versaTo change a percentage into a fraction or a decimal, divide it by 100%Example 11Convert the following percentages into decimals
Percentages in Daily LifeApply percentages in daily lifeExample 12In an assignment, Regina scored 9 marks out of 12. Express this as a percentageSolution
Example 13A school has 400 students of which 250 are girls. What percentage of the students are not girls?Solution
