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SS1: MATHEMATICS - 1ST TERM

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  1. Number Base System I | Week 1
    6 Topics
    |
    2 Quizzes
  2. Number Base System II | Week 2
    3 Topics
  3. Number Base System III | Week 3
    2 Topics
    |
    1 Quiz
  4. Modular Arithmetic I | Week 4
    2 Topics
  5. Modular Arithmetic II | Week 5
    2 Topics
  6. Modular Arithmetic III | Week 6
    3 Topics
    |
    1 Quiz
  7. Indices I | Week 7
    3 Topics
  8. Indices II | Week 8
    1 Topic
    |
    1 Quiz
  9. Logarithms I | Week 9
    3 Topics
  10. Logarithms II | Week 10
    4 Topics
    |
    1 Quiz



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Lesson 7, Topic 1
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Revision of Standard Form

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A number is said to be in standard form if the number is expressed in the form 

A × 10n

Where A is a number between 1 and 10. 

This is often written as 1 < A < 10 n is an integer (Positive or Negative)

In standard form, power of 10 (i.e. 10n) is often used. 

Examples of positive powers of 10 are:

1 = 100 

100 = 102 

1000 = 103 etc 

Examples of negative powers of 10 

10-1 = \( \frac{1}{10} \scriptsize \: or \: 0.1 \)

10-2  = \( \frac{1}{100} \scriptsize \: or \: 0.01 \)

10-3  =\( \normalsize \frac{1}{1000} \scriptsize \: or \: \normalsize \frac{1}{10^3} \scriptsize = 0.001 \)

Hence 3500000 can be written in standard form as 3.5 × 106

Screen Shot 2021 03 08 at 10.09.23 AM

Similarly, the number 0.00000067 can be written as 6.7 × 10-7 

Example

Express the following numbers in standard form

(a) 5467
(b) 67894
(c)0.000456
(d) 0.00469

Solution

(a) \( \scriptsize 5467 \\ \scriptsize = 5.467 \: \times \: 1000\\ \scriptsize = 5.467 \: \times \: 10^3 \)

(b) \( \scriptsize 67894 \\ \scriptsize = 6.7894 \: \times \: 10000\\ \scriptsize = 6.7894 \: \times \: 10^4 \)

(c) \( \scriptsize 0.000456 \\ \scriptsize = 4.56 \: \times \: 0.0001 \\ \scriptsize = 4.56 \: \times \: 10^{-4} \)

(d) \( \scriptsize 0.00469 \\ \scriptsize = 4.69 \: \times \: 0.001 \\ \scriptsize = 4.69 \: \times \: 10^{-3} \)

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