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

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**Standard Form 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

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**Imagine the difficulty of calculating the mass of 1 mole of electrons!**

kg x ???????????????????????????????????

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Standard Form: A method of representing very large or very small numbers in the form: M x 10n 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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. 9 8 7 6 5 4 3 2 1 Step 1: Insert an understood decimal point Step 2: Decide where the decimal must end up so that one number is to its left Step 3: Count how many places you bounce the decimal point Step 4: Re-write in the form M x 10n

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2.5 x 109 The exponent is the number of places we moved the decimal.

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**0.0000579 1 2 3 4 5 Step 2: Decide where the decimal must end**

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

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5.79 x 10-5 The exponent is negative because the number we started with was less than 1.

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**More Examples Use: 2.898 (moved 8 places to the left)**

Given: 289,800,000 Use: (moved 8 places to the left) Answer: x 108 Given: Use: 5.67 (moved 4 places to the right) Answer: 5.67 x 10–4 Timberlake lecture plus

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Learning Check Express these numbers in standard form: 1) 2) 3) 4) 2 5) Timberlake lecture plus

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Solution Express these numbers in standard form: 1) x 105 2) x 10–3 3) 3 x 109 4) 2 x 100 5) x 10–1 Timberlake lecture plus

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**Coming out of Standard Form**

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.

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**Examples Use: 5,093,000 (moved 6 places to the right)**

Given: x 106 Use: 5,093, (moved 6 places to the right) Given: x 10–4 Use: (moved 4 places to the left) Timberlake lecture plus

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**PERFORMING CALCULATIONS IN STANDARD FORM**

ADDITION AND SUBTRACTION

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**Review: M x 10n Standard form expresses a number in the form:**

n is an integer 1 M 10

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IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged. 4 x 106 + 3 x 106 7 x 106

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**The same holds true for subtraction in standard form.**

4 x 106 - 3 x 106 1 x 106

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**If the exponents are NOT the same, we must move a decimal to make them the same.**

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4.00 x 106 4.00 x 106 x 105 + .30 x 106 4.30 x 106 Move the decimal on the smaller number!

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A Problem for you… 2.37 x 10-6 x 10-4

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Solution… x 10-6 2.37 x 10-6 x 10-4

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Solution… x 10-4 x 10-4 x 10-4

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