# Places to the left if n is a negative integer if

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places to the left if n is a negative integer. If necessary additional zeros are inserted to make up the required number of decimal places. 11 Engineering Mathematics: Open Learning Unit Level 0 1.2: Basic Algebra

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Then, for example, the number 5000 can be written 5 × 1000 = 5 × 10 3 the number 403 can be written 4 . 03 × 100 = 4 . 03 × 10 2 the number 0.009 can be written 9 × 0 . 001 = 9 × 10 - 3 Now do this exercise Write the number 0.00678 in scientific notation. Answer Example Engineering Constants Many constants appearing in engineering calculations are expressed in scientific notation. For example the charge on an electron equals 1 . 6 × 10 - 19 coulomb and the speed of light is 3 × 10 8 ms - 1 . Avagadro’s constant is equal to 6 . 023 × 10 26 and is the number of atoms in one kilomole of an element. Clearly the use of scientific notation avoids writing lengthy strings of zeros. Your scientific calculator will be able to accept numbers in scientific notation. Often the E button is used and a number like 4 . 2 × 10 7 will be entered as 4 . 2 E 7. Note that 10E4 means 10 × 10 4 , that is 10 5 . To enter the number 10 3 say, you would key in 1 E 3. Entering powers of 10 incorrectly is a common cause of error. You must check how your particular calculator accepts numbers in scientific notation. Now do this exercise Use your calculator to find 4 . 2 × 10 - 3 × 3 . 6 × 10 - 4 . This exercise is designed to check that you can enter numbers given in scientific notation into your calculator. Answer More exercises for you to try 1. Express each of the following numbers in scientific notation: a) 45, b) 456, c) 2079, d) 7000000, e) 0 . 1, f) 0 . 034, g) 0.09856 2. Simplify 6 × 10 24 × 1 . 3 × 10 - 16 Answer Engineering Mathematics: Open Learning Unit Level 0 1.2: Basic Algebra 12
End of Block 1.2 13 Engineering Mathematics: Open Learning Unit Level 0 1.2: Basic Algebra

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1. a) 27, b) 243, c) 32, 2. a) 0.04, b) 225 3. a) 343, b) 4651.7. 4. a) 7 5 , b) t 4 , c) ( 1 2 ) 2 ( 1 7 ) 3 5. a) 4 9 , b) 8 125 , c) 1 4 , d) 1 8 , e) 0 . 1 3 means (0 . 1) × (0 . 1) × (0 . 1) = 0 . 001 Back to the theory Engineering Mathematics: Open Learning Unit Level 0 1.2: Basic Algebra 14
All quantities have the same base. To multiply the quantities together, the indices are added: y 9 Back to the theory 15 Engineering Mathematics: Open Learning Unit Level 0 1.2: Basic Algebra

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(a) The bases are the same, and the division is carried out by subtracting the indices: 5 9 - 7 = 5 2 = 25 (b) y 5 - 2 = y 3 Back to the theory Engineering Mathematics: Open Learning Unit Level 0 1.2: Basic Algebra 16
x 2 × 5 = x 10 Back to the theory 17 Engineering Mathematics: Open Learning Unit Level 0 1.2: Basic Algebra

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Again, using the third law, the two powers are multiplied: e x × y = e xy Back to the theory Engineering Mathematics: Open Learning Unit Level 0 1.2: Basic Algebra 18

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• Winter '10
• John Schaefer
• Math, Open Learning, Open Learning Unit, Learning Unit Level

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