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

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

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

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

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.

. 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

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

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

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

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

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

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

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.

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

PERFORMING CALCULATIONS IN STANDARD FORM

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

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

The same holds true for subtraction in standard form.
4 x 106 - 3 x 106 1 x 106

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

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

A Problem for you… 2.37 x 10-6 x 10-4

Solution… x 10-6 2.37 x 10-6 x 10-4

Solution… x 10-4 x 10-4 x 10-4