- 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.**