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## Math : Operations on Positive and Negative Integers

The Civil Service Exam includes questions on integers. There may be questions involving integers as well as a flow chart which makes use of integers (more on that flow chart thing next time). Let’s start with the basics first.

**Integers** are zero plus all the positive and negative whole numbers (0, 345, -678, 43, -26, etc.). They can be represented on a number line with zero in the middle. To the left are all the negative integers and to the right are all the positive integers. Remember that integers do not have a fractional part. (more…)

## Basic Math : What is PEMDAS ?

**PEMDAS** (or what others remember as Please Excuse My Dear Aunt Sally) is simply an acronym which stands for ‘Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction’. If you have a number sentence with two or more operations, the order of the letters in PEMDAS tells you how to go about these operations. It tells you what to calculate first, second, third and so on, until everything is done.

PEMDAS serves as a guideline so all of us can obtain only one correct answer in a math expression. Without PEMDAS, we can end up having two or more different answers to a single equation.

For example, 5 + 4 x 3 = ?

**WITHOUT PEMDAS,**

- We can do the addition first and get: 9 x 3 = 27
- or we can do the multiplication first and get 5 + 12 = 17

## Math : Conversion of Percentages to Decimals and Fractions – Lesson 3

This lesson is part of the **Lesson on Conversion Series**. The conversion of Percentages to Decimals or Fractions is usually part of the set of questions on numerical ability. You may also need this skill when solving word problems on ratio and proportion, and on word problems involving discounts, interest, and profit.

Before we begin our lesson, let me again remind you some basic points to remember when converting Fractions, Decimals, and Percent:

- In a fraction, the top number is the Numerator and the bottom number is the Denominator.
- Be careful when counting the decimal places. Here, decimal place refers to the number of digits to the right of a decimal point. So, in 0.25, 25 has two decimal places; in 0.001, 1 has three decimal places; in 0.058, 58 has three decimal places; and in 0.06, 6 has two decimal places.
- The number to the left of the decimal point is the integer. The number to the right of the decimal point is the fractional part.
- ‘Percent’ is a number or ratio expressed as a fraction of 100.

### Converting a Percent to a Decimal:

- Simply move the decimal point two places to the left.
- Remove the percent sign.

Examples:

- 25% = 0.25
- 9% = 0.09

### Converting a Percent to a Fraction:

- Remove the percent sign.
- Find the numerator: The number is the numerator
- Find the denominator: The denominator is always 100 unless the number has a fractional part.
- If the number has a fractional part (refers to numbers to the right of the decimal point), count the decimal places and then remove the decimal point.

The number of decimal places indicates the number of zeroes you need to add to the denominator – 100.

Examples:

- 25% = ?

Find the numerator: 25

Find the denominator: 100 (because 25% has no fractional part)

Thus 25% = 25/100 - 0.8% = ?

Find the numerator: 8

Find the denominator: 0.8 is a fractional part, and there is 1 decimal place. So you add 1 zero to 100, making it 1000.

Thus 0.8% = 8/1000

The Lesson Series on Conversion

## Math : Conversion of Decimals to Fractions, and Percentages – Lesson 2

This lesson is part of the **Lesson on Conversion Series**. Converting Decimals to Fractions, and/ or Percentages are usually part of questions on numerical ability.You may also need this skill when dealing with word problems involving ratio and proportion, and money problems involving discounts, interest, and profit.

Before we go on with our lesson, let me again remind you some basic points to remember when converting Fractions, Decimals, and Percent:

- In a fraction, the top number is the Numerator and the bottom number is the Denominator.
- Be careful when counting the decimal places. Here, decimal place refers to the number of digits to the right of a decimal point. So, in 0.25, 25 has two decimal places; in 0.001, 1 has three decimal places; in 0.058, 58 has three decimal places; and in 0.06, 6 has two decimal places.
- The number to the left of the decimal point is the integer. The number to the right of the decimal point is the fractional part.
- ‘Percent’ is a number or ratio expressed as a fraction of 100.

### Converting a Decimal to a Fraction:

- Find the numerator: The number that you have without the decimal point is the numerator.
- Find the denominator: Count the decimal places (remember what I taught you earlier). If there is only one decimal place, the denominator is 10. If there are two decimal places, the denominator is 100. If there are three places, the denominator is 1000. If you can see the pattern, it’s 1+ the number of zeroes depending on the decimal places.
- If there is a number to the left of the decimal point (an integer), just attach it to the resulting fraction afterwards.

Examples:

- 0.25 = ?

Find the numerator: 25

Find the denominator: 0.25 = two decimal places = two zeroes = 100

Thus 0.25 = 25/100 - 1.33 = ?

Remove the integer (The integer is 1)

Find the numerator: 33

Find the denominator: 0.33 = two decimal places = two zeroes = 100

Thus 0.33 = 33/100

Attach the integer, Thus,1.33 = 1 33/100

### Converting a Decimal to a Percent:

- Simply move the decimal point two places to the right
- Attach a percentage sign.

Examples:

- 0.25 = 25%
- 0.08 = 08 % or 8%
- 0.9 = 0.90 = 90%
- 1.43 = 143%

The Lesson Series on Conversion

## Math : Conversion of Fractions to Decimals, and Percentages – Lesson 1

This lesson is part of the **Lesson on Conversion Series**. Converting Fractions to Decimals or Percentages is usually part of the set of questions on numerical ability. You may also need this skill when solving word problems involving ratio and proportion, and money problems involving discounts, interest, and profit.

Before we go to our lesson, let me again remind you some basic points to remember when converting Fractions, Decimals, and Percent:

- In a fraction, the top number is the Numerator and the bottom number is the Denominator.
- Be careful when counting the decimal places. Here, decimal place refers to the number of digits to the right of a decimal point. So, in 0.25, 25 has two decimal places; in 0.001, 1 has three decimal places; in 0.058, 58 has three decimal places; and in 0.06, 6 has two decimal places.
- The number to the left of the decimal point is the integer. The number to the right of the decimal point is the fractional part.
- ‘Percent’ is a number or ratio expressed as a fraction of 100.

### Converting a Fraction to a Decimal:

- Simply divide the numerator by the denominator.
- Be careful with the decimal places.

Examples:

- 1/4 = 1 (numerator) ÷ 4 (denominator) = 0.25
- 3/2 = 3 (numerator) ÷ 2 (denominator) = 1.50
- 5/8 = 5 (numerator) ÷ 8 (denominator) = 0.625

### Converting a Fraction to a Percent:

- Multiply the numerator by 100.
- Divide the resulting product by the denominator.
- Attach the percentage sign.

Examples:

- 1/4 = ?

1 x 100 = 100 (1 is the numerator x 100)

100 ÷ 4 (4 is the denominator)

= 25% (Attach the percentage sign) - 3/8 = ?

3 x 100 = 300 (3 is the numerator x 100)

300 ÷ 8 (8 is the denominator)

= 37.5% (Attach the percentage sign)

The Lesson Series on Conversion

## Math : Conversion of Fraction, Decimals, and Percent – Lesson Series

Fractions to Decimals, Fractions to Percentages, Decimals to Fractions, Decimals to Percentages, Percent to Decimals, and Percent to Fractions – You have to get used to converting one into another if you want to pass the Civil Service Exam.

So to get you started, let me start by saying that **Decimals, Fractions and Percentages** are just like Number Synonyms. For example, 0.25, 1/4, and 25% – **they all tell you the SAME THING**. They are simply different ways of showing a part of a ‘whole’. That being said, it is EASY to convert their values if you just remember the right steps. Remember that what we discuss here are quick and easy steps that will help you deal with the CSE Math questions.

**Basic points to remember when converting Fractions, Decimals, and Percent**:

- In a fraction, the top number is the
**Numerator**and the bottom number is the**Denominator**. - Be careful when counting the
**decimal places**. Here, decimal place refers to the number of digits to the right of a decimal point. So, in 0.25, 25 has two decimal places; in 0.001, 1 has three decimal places; in 0.058, 58 has three decimal places; and in 0.06, 6 has two decimal places. - The number to the left of the decimal point is the
**integer**. The number to the right of the decimal point is the**fractional part**. - ‘Percent’ is a number or ratio expressed as a fraction of 100.

Now onto the conversion (Please click on the links below)…

**Converting a Fraction to a Decimal, Converting a Fraction to a Percent**

**Converting a Decimal to a Fraction, Converting a Decimal to a Percent**

**Converting a Percentage to a Decimal, Converting a Percentage to a Fraction**

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