Table of Contents

**Difference between Whole Numbers and Decimal Numbers**

Whole number is a number without fraction. For example 1, 2, 3, 41000, 38888 are examples of whole numbers.71/2 is not a whole number. A decimal number is a fractional number less than 1. It is smaller to a whole number. Examples – 0.1,0.01,0.001etc

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**Whole Numbers in Standard Form and Decimal Numbers in Standard Form**

Whole numbers in standard form are expressed in the form of A x 10^{n} such that A is a number between 1 and 10, n is a whole number.

Example

Express the following in standard form (a) 200 (b) 4100 (c) 300000

Solution

- 200 = 2 x 100 = 2×10
^{2} - 4100 = 4.1 x 1000 = 4.1 x 10
^{3} - 300000 = 3 x 100000 = 3 x 10
^{5}

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**Evaluation**

Express the following in standard form (a) 500 (b) 36000 (c) 7200000

Decimal fractions such as 0.00 and 0.000001 can be expressed as powers of 10 e.g. 0.0001 = 1/10000 = 1/10^{4 }= 10^{-4 }

Thus, any decimal fraction can be expressed in a standard form e.g. 0.008=8/1000=8/10^{3 }=8×1/10^{3}=8×10^{-3}

Therefore, the number 8×10^{-3 }is in standard form ax10 and n is a negative integer while A is a number between1 and 10

Example

Express the following in standard form (a) 0.0023 (b) 0.00034 (c) 0.125

Solution

- 023 = 23/1000 = 2.3/10
^{2}= 2.3 x 10^{-3} - 00034 34/100000= 3.4/10
^{4}= 3.4x 10^{-4} - 125 = 125/1000 = 1.25/10
^{1}= 1.25×10^{-1}

**Evaluation**

Express the following in standard form (a) 0.0067 (b) 0.00082 (c) 0.012

**FACTORS, MULTIPLES AND PRIME NUMBERS**

The factors of a number are the whole numbers that divide the number exactly. For example the factors of 10 are 1, 2 and 5.

A prime number has only two factors, itself and 1. The following are examples of prime numbers 2, 3, 5, 7, 11,13 . However, 1 is not a prime number.

A multiple of a whole number is obtained by multiplying it by any whole number.

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**Example **

- Write down all the factors of 18.
- State which of theses factors are prime numbers
- Write the first three multiples of 18
- Express 18 as a product of its prime factors in index form

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**Solution:**

- Factors of 18:1, 2,3,6,9 and 18.
- Prime numbers of the factors of 18:2 and3
- The first three multiples of 18 are 1×18 = 18, 2×18=36, 3×18=54 => 18, 36 and 54.
- 18 = 2x3x3 = 2 x 3
^{2}in index form

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**Example 2:**

- Write down all the factors of 22.
- State which of theses factors are prime numbers
- Write the first three multiples of 22

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**Solution:**

- Factors of 22:1, 2, and 11.
- Prime numbers of the factors of 22: 2 and11
- The first three multiples of 22 are 1×22 = 22, 2×22=44, 3×22=66 => 22, 44 and 66.

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**Evaluation **

- Write down all the factors
- State which of theses factors are prime numbers
- Write the first three multiples of each of the following numbers below
- Express each as a product of its prime factors in index form

- 12 (2) 30 (3) 39 (4) 48

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**WEEKEND ASSIGNMENT **

- Which of these is not a prime number (a) 2 (b) 5 (c) 7 ( d) 1
- Express 360000 in standard form (a) 3.6 x 10
^{5}(b) 3.6 x 10^{6}(c) 3.6 x 10^{3}( d) 3.6 x 10^{4} - Express 0.000045 in standard form (a) 4.5 x 10
^{-2 }(b) 4.5 x 10^{3 }(c) 4.5 x 10^{-5 }(d) 4.5 x 10^{-6} - Which of these is not a factor of 42 (a) 9 (b) 6 (c) 7 (d) 2
- Express 50 is product of its prime factor (a) 2 x 5
^{2}(b) 2 x 5 (c) 2^{2 }x 5^{2}(d) 2 x 5

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**THEORY**

- For each number 42,45,48,50
- Write down all its factors.
- State which factors are prime numbers?
- Express the number as a product of its prime factors.
- Express the following in standard form (a) 345000 (b) 0.00034 (c) 0.125

See also