NATURAL NUMBERS
NATURAL NUMBERS :Specific Objectives
By the end of the topic the learner should be able to:
- Identify, read and write natural numbers in symbols and words;
- Round off numbers to the nearest tens, hundreds, thousands, millions and billions;
- Classify natural numbers as even, odd or prime;
- Solve word problems involving natural numbers.
Content
- Place values of numbers
- Rounding off numbers to the nearest tens, hundreds, thousands, millions and billions
- Odd numbers
- Even numbers
- Prime numbers
- Word problems involving natural numbers
Introduction
Place value
A digit 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.
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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).
- 389,410 ,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.
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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, 3189 to the nearest is 3190.
When rounding off to the nearest 100, 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, 3189 is 3200.
Example
Rounding off each of the following numbers to the nearest number indicated in the bracket:
- 473,678 ( 100)
- 524,239 (1000)
- 2,499 (10)
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
7180
6349
259
+ 79542
86150
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Subtracting
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
X 63
1407
+ 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 11 is the remainder
Note:
6493 = (463 x 14) + 11
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 |
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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 = 312,210 kg
2654 bags weigh 2654 x 90 = 238,860 kg
Amount of maize left = 312,210 – 238,860
= 73,350 kg.
- Number of bags = 815 + 468
=1283
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. 471,123, 1197,7129.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, 11, 13, 17 and 19.
Note:
- 1 is not a prime number.
- 2 is the only even number which is a prime number.
End of topic
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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.
ALL MATHMATICS NOTES FORM 1-4 WITH TOPICAL QUESTIONS & ANSWERS
