Practice questions 13.5


1. Solve for n in the following. (i) 2 n + 6


= 2 5


2. Solve for x in the following. (i) 6 2x + 6


= 6 4x + 12


3. Solve for x in the following. (i) 4 3x − 2


= 1


4. Solve for n in the following. (i) 2 n


= 2 7 __


4 13.6 Scientifi c notation (ii) 3 6n + 18 (ii) 2 6x − 14 (ii) 3 1 − 2x (ii) 2 n − 5 = 3 6 = 2 2x−10 = 243


= 1 __


8 (iii) 4 5n − 10 = 4 30 (iii) p10x − 10 (iii) 4 x + 2 (iii) 5 n = p− 4x + 18 = 64


= 125 ___


√


_ 5


By the end of this section you should be able to:


● understand how to write numbers in scientifi c (index) notation


In Linking Thinking 1, we dealt with writing numbers greater than or equal to 1 in index notation. We will now also look at writing numbers less than 1 and greater than 0.


Writing a number in index form a × 10 n 1


where 1 ≤a< 10


Move the decimal place to the left or right until the fi rst digit is equal to or greater than 1 and less than 10.


2 3


Count the number of times you had to move the decimal place to the left or right in Step 1. Call this value n .


Write × 10 n ●


● after the number you found in Step 1.


n is positive if you moved the decimal place to the left. n is negative if you moved the decimal place to the right.


Worked example 1 Write the following in scientifi c (index) notation. (i) 85 470 000


Solution (i)


Remember: Scientifi c (or index) notation is when a number is written in the form a × 10 n


a is a number equal to or greater than 1 and less than 10 ( 1 ≤ a < 10 ) and n ∈ℤ .


, where


(ii) 0·0005678


(iii)


0·00400687


(ii)


(iii)


Using your calculator to perform operations on numbers in scientifi c (index) notation To type a number into your calculator in index form, you must use the × 10 n you use depends on which brand of calculator you use. To enter 1 ⋅ 3 × 102


OR Section B Advancing mathematical ideas 221


or Exp button. Which button into the calculator:


13 Indices


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