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Standard Form Standard Form (also referred to as "scientific notation“)

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In science, we deal with some very LARGE numbers: 1 mole = In science, we deal with some very SMALL numbers: Mass of an electron = kg Standard Form

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Imagine the difficulty of calculating the mass of 1 mole of electrons! kg x x ???????????????????????????????????

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Standard Form: A method of representing very large or very small numbers in the form: M x 10 n M x 10 n M is a number between 1 and 10 n is an integer For very large numbers and very small numbers, standard form is more concise.

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Step 1: Insert an understood decimal point. Step 2: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step 3: Count how many places you bounce the decimal point the decimal point Step 4: Re-write in the form M x 10 n

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2.5 x 10 9 The exponent is the number of places we moved the decimal.

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Step 2: Decide where the decimal must end up so that one number is to its left up so that one number is to its left Step 3: Count how many places you bounce the decimal point the decimal point Step 4: Re-write in the form M x 10 n 12345

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5.79 x The exponent is negative because the number we started with was less than 1.

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Timberlake lecture plus9 More Examples Given: 289,800,000 Use: (moved 8 places to the left) Answer: x 10 8 Given: Use: 5.67 (moved 4 places to the right) Answer: 5.67 x 10 –4

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Timberlake lecture plus10 Learning Check Express these numbers in standard form: 1) ) ) ) 2 5)

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Timberlake lecture plus11 Solution Express these numbers in standard form: 1) x ) x 10 –3 3) 3 x ) 2 x ) x 10 –1

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Move the decimal place to the right for a positive exponent 10. Move the decimal place to the left for a negative exponent 10. Use zeros to fill in places. Coming out of Standard Form

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Timberlake lecture plus13 Examples Given: x 10 6 Use: 5,093,000 (moved 6 places to the right) Given: x 10 –4 Use: (moved 4 places to the left)

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PERFORMING CALCULATIONS IN STANDARD FORM ADDITION AND SUBTRACTION

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Review: Standard form expresses a number in the form: M x 10 n 1 M 10 n is an integer

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4 x x 10 6 IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged. 7 x 10 6

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4 x x 10 6 The same holds true for subtraction in standard form. 1 x 10 6

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4 x x 10 5 If the exponents are NOT the same, we must move a decimal to make them the same.

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4.00 x x x x 10 6 Move the decimal on the smaller number! 4.00 x 10 6

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A Problem for you… 2.37 x x 10 -4

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2.37 x x Solution… x 10 -6

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x Solution… x x 10 -4

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