- Introduction
- Rounding Off
- Operations on Whole Numbers
- Even Number
- Odd Number
- Prime Number
- Past KCSE Questions on the Topic

## Introduction

### Place Value

- A digit can have a different value in a number because of its position in a number. The position of a digit in a number is called its
**place value.**

### Total Value

- This is the product of the digit and its place value.

**Example**

Number | Hundred Millions | Ten Millions | Millions | Hundred Thousands | Ten Thousands | Thousands | Hundred | Tens | ones |

345,678,901 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 | 1 |

769,301 ,854 | 7 | 6 | 9 | 3 | 0 | 1 | 8 | 5 | 4 |

902,350,409 | 9 | 0 | 2 | 3 | 5 | 0 | 4 | 0 | 9 |

- A place value chart can be used to identify both place value and total value of a digit in a number. The place value chart is also used in writing numbers in words.

**Example**

- Three hundred and forty five million, six hundred and seventy eight thousand, nine hundred and one.
- Seven hundred and sixty nine million, Three hundred and one thousand, eight hundred and fifty four.

### Billions

- A billion is one thousands million, written as 1, 000, 000,000.There are ten places in a billion.
**Example**

What is the place value and total value of the digits below?- 47,397,263,402 (place value 7 and 8).
- 389,41 0 ,000,245 ( place 3 and 9)

**Solution**- The place value for 6 is ten thousands. Its total value is 60,000.
- The place value of 3 is hundred billions. Its total value is 300,000,000,000.

## Rounding Off

- When rounding off to the nearest ten, the ones digit determines the ten i.e. if the ones digit is 1 , 2, 3, or 4 the nearest ten is the ten number being considered.
- If the ones digit is 5 or more the nearest ten is the next ten or rounded up.
- Thus 641 to the nearest ten is 640, 31 89 to the nearest is 31 90.
- When rounding off to the nearest 1 00, then the last two digits or numbers end with 1 to 49 round off downwards.
- Number ending with 50 to 99 are rounded up.
- Thus 641 to the nearest hundred is 600, 31 89 is 3200.
**Example**Rounding off each of the following numbers to the nearest number indicated in the bracket:- 473,678 ( 1 00)
- 524,239 (1 000)
- 2,499 (1 0)

**Solution**- 473,678 is 473,700 to the nearest 100.
- 524,239 is 524,000 to the nearest 1000
- 2,499 is 2500 to the nearest 10.

## Operations on Whole Numbers

### Addition

**Example**

Find out:

- 98 + 6734 + 348
- 6349 + 259 +7954

**Solution**

- Arrange the numbers in vertical forms

98

6734

+348

71 80 - 6349

259

+79542

86150

### Subtraction

**Example**

Find: 73469 – 8971

**Solution**

73469

-8971

64498

### Multiplication

- The product is the result of two or more numbers.

**Example**

Work out: 469 x 63

**Solution**

469

×63

1407 → 469 x 3 = 1407

+28140→469 x 60 = 28140

29547

### Division

- When a number is divided by the result is called the quotient. The number being divided is the divided and the number dividing is the divisor.

**Example**

Find: 6493 ÷ 14

**Solution**

We get 463 and 1 1 is the remainder

**Note:**

6493 = (463 x 14) + 1 1

In general, dividend = **quotient x division + remainder.**

Operation | Words |

Addition | sum plus added more than increased by |

Subtraction | difference minus subtracted from less than decreased by reduced by deducted from |

Multiplication | product of multiply times twice thrice |

Division | quotient of divided by |

Equal | equal to result is is |

### Word Problem

- In working the word problems, the information given must be read and understood well before attempting the question.
- The problem should be broken down into steps and identify each other operations required.

**Example**

Otego had 3469 bags of maize, each weighing 90 kg. He sold 2654 of them.

- How many kilogram of maize was he left with?
- If he added 468 more bags of maize, how many bags did he end up with?

**Solution**

- One bag weighs 90 kg.

3469 bags weigh 3469 x 90 = 31 2,21 0 kg

2654 bags weigh 2654 x 90 = 238,860 kg

Amount of maize left = 31 2,21 0 – 238,860

= 73,350 kg. - Number of bags = 81 5 + 468

=1 283

## Even Number

- A number which can be divided by 2 without a remainder E.g. 0,2,4,6 0 or 8

3600, 7800, 806, 78346

## Odd Number

- Any number that when divided by 2 gives a remainder. E.g. 471 ,1 23, 1 1 97,71 29.The numbers ends with the following digits 1 , 3, 5,7 or 9.

## Prime Number

- A prime number is a number that has only two factors one and the number itself.
- For example, 2, 3, 5, 7, 1 1 , 1 3, 1 7 and 1 9.

Note:- is not a prime number.
- is the only even number which is a prime number.

## Past KCSE Questions on the Topic

- Write 27707807 in words
- All prime numbers less than ten are arranged in descending order to form a number
- Write down the number formed
- What is the total value of the second digit?
- Write the number formed in words

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