Presentation on theme: "Standard Form (also referred to as "scientific notation“)"— Presentation transcript:
1Standard Form (also referred to as "scientific notation“)
2Standard 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
3Imagine the difficulty of calculating the mass of 1 mole of electrons! kgx???????????????????????????????????
4Standard Form:A method of representing very large or very small numbers in the form:M x 10nM is a number between 1 and 10n is an integerFor very large numbers and very small numbers, standard form is more concise.
5.987654321Step 1: Insert an understood decimal pointStep 2: Decide where the decimal must endup so that one number is to its leftStep 3: Count how many places you bouncethe decimal pointStep 4: Re-write in the form M x 10n
62.5 x 109The exponent is the number of places we moved the decimal.
70.0000579 1 2 3 4 5 Step 2: Decide where the decimal must end up so that one number is to its leftStep 3: Count how many places you bouncethe decimal pointStep 4: Re-write in the form M x 10n
85.79 x 10-5The exponent is negative because the number we started with was less than 1.
9More Examples Use: 2.898 (moved 8 places to the left) Given: 289,800,000Use: (moved 8 places to the left)Answer: x 108Given:Use: 5.67 (moved 4 places to the right)Answer: 5.67 x 10–4Timberlake lecture plus
10Learning CheckExpress these numbers in standard form:1)2)3)4) 25)Timberlake lecture plus
11SolutionExpress these numbers in standard form:1) x 1052) x 10–33) 3 x 1094) 2 x 1005) x 10–1Timberlake lecture plus
12Coming 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.
13Examples Use: 5,093,000 (moved 6 places to the right) Given: x 106Use: 5,093, (moved 6 places to the right)Given: x 10–4Use: (moved 4 places to the left)Timberlake lecture plus
14PERFORMING CALCULATIONS IN STANDARD FORM ADDITION AND SUBTRACTION
15Review: M x 10n Standard form expresses a number in the form: n is an integer1 M 10
16IF 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 1067x 106
17The same holds true for subtraction in standard form. 4 x 106- 3 x 1061x 106
18If the exponents are NOT the same, we must move a decimal to make them the same.
194.00 x 1064.00 x 106x 105+ .30 x 1064.30x 106Move the decimal on the smaller number!