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SIGNIFICANT FIGURE (SF)

 Example of SF

71 = 2 SF      53.19 = 4 SF       3.07 = 3 SF       4.70 = 3 SF       0.07 = 1 SF

20.00 = 4 SF   0.01230 = 4 SF         20 = 1 SF            700 = 1 SF

   ALL NON-ZERO DIGITS ARE SIGNIFICANT
•   ALL ZEROS BETWEEN NON-ZERO DIGITS ARE SIGNIFICANT
•   ALL ZEROS AFTER ANY NON-ZERO DIGIT IN A DECIMAL ARE SIGNIFICANT
•   ALL ZEROS BEFORE ANY NON-ZERO DIGIT IN A DECIMAL ARE NOT SIGNIFICANT
• ALL ZEROS AFTER ANY NON-ZERO DIGIT IN A WHOLE NUMBER  ARE NOT SIGNIFICANT UNLESS STATED OTHERWISE

 

1. ROUNDING OFF NUMBERS

 

84.56 = 84.6 ( 3 SF)  

7.0142 = 7.014 (4 SF)

0.00159 = 0.002(4 SF) or 0.0016 (5 SF)

2. STANDARD FORM
 
  •  THE FIRST NUMBER MUST BE CHANGED TO A DIGIT THAT IS BETWEEN 1 TO 9 ONLY AND TO BE MULTIPLIED BY AN INDEX

780300 = 7.803 X 10⁵  * THE DECIMAL POINT MOVES 5 TIMES TO THE LEFT

0.07901 = 7.901 X 10⁻²   * THE DECIMAL POINT MOVES 2 TIMES TO THE RIGHT

5.041 X 10³ = 5041  * THE DECIMAL POINT MOVES 3 TIMES TO THE RIGHT

7.0063 X 10⁵ = 700630 * THE DECIMAL POINT MOVES 5 TIMES TO THE RIGHT

8.61 X 10⁻³ = 0.00861 * THE DECIMAL POINT MOVES 3 TIMES TO THE LEFT

3. COMPUTATION OF NUMBERS IN STANDARD FORM

 

  • TWO NUMBERS IN STANDARD FORM CAN BE ADDED OR SUBTRACTED IF BOTH NUMBERS HAVE THE SAME INDEX    a x 10ⁿ + b x 10ⁿ = (a + b) x 10ⁿ

3.5 x 10³ + 2.103 x 10³ = ( 3.5 + 2.103 ) x 10³ = 5.603 x 10³

5.89 x 10⁻³ – 2.01 x 10⁻³ = ( 5.89 – 2.01 ) x 10⁻³ = 3.88 x 10⁻³

5.6 x 10⁵ + 2.41 x 10⁷ = 0.056 x 10⁷ + 2.41 x 10⁷

                                   = ( 0.056 + 2.41 ) x 10⁷ = 2.456 x 10⁷

3.4 x 10⁻⁴ – 8 x 10⁻⁵ = 3.4 x 10⁻⁴ – 0.8 x 10⁻⁴ 

                              = ( 3.4 – 0.8 ) x 10⁻⁴  = 2.6 x 10⁻⁴

  • WHEN TWO NUMBERS IN STANDARD FORM ARE MULTIPLIED OR DIVIDED, THE ORDINARY NUMBERS ARE MULTIPLIED OR DIVIDED WITH EACH OTHER WHILE THEIR INDICES ARE ADDED OR SUBTRACTED

(a x 10³) x (b x 10⁵) = (a x b) x 10³⁺⁵ = ab x 10

(a x 10⁹) ÷ (b x 10⁵) =  (a ÷ b) x 10⁹⁻⁵ =  a/b x 10

9.5 x 10³ x 2.2 x 10² = (9.5 x 2.2) x 10³⁺²

= 20.9 x 10⁵ = 2.09 x 10¹ x 10⁵

= 2.09 x 10¹⁺⁵ = 2.09 x 10⁶

(7.2 x 10⁵) ÷ (6 x 10⁻²) = (7.2/6) x 10⁵⁻⁽⁻²⁾ = 1.2 x 10⁵⁺² = 1.2 x 10⁷