Scientific Notation

Definition Scientific notation is defined as a standardized way to represent any number as the product of a real number and a power of 10. Its standard form is: a x 10b

Parts of the scientific notation expression

Why Scientific Notation? Imagine if you have to write the number for the charge of a single electron out a few times qe = 0.000000000000000000162 C So we came up with a shorter way to represent the same number but without so many 0s. qe = 1.62 x 10 -19 C

Important rules to Scientific Notation Rules: 1. The base is always 10 2. The exponent is a non-zero integer (+ or -) 3. The absolute value of the coefficient is greater than or equal to 1 and strictly less than 10 4. The coefficient carries the sign (+ or -) 5. The Mantissa carries the rest of the significant digits.

Finding The Scientific Notation Form Most scientific calculators will put any number into scientific notation, but if you have to do it by hand, there is a simple procedure: 1. With the number in its original form, start at the decimal point and count the spaces between digits, either left or right, until you get to the first non-zero digit. 2. If you are moving right, go one additional space so that there is a whole number on the left and a mantissa on the right

Finding The Scientific Notation Form 3. If you are moving left, keep counting until you have just one whole number on the left 4. The number of spaces you move becomes the exponent. If you moved right, the exponent is negative. If left, the exponent is positive. If the exponent is zero, you don't really need scientific notation. 5. If you have a number (or a result) that is not quite in standard form because the mantissa is 10 or greater or less than 1, you can correct it. Count left or right from the decimal point until you have just one whole number on the left. If you moved left, then add that number to the existing exponent. If right, then subtract.

Changing the charge of an electron to scientific notation

Doing Arithmetic Operations with Scientific Notation To multiply two numbers, multiply the coefficients and add the exponents. To divide two numbers, divide the coefficients and subtract the exponent of the divisor from the exponent of the dividend. You can add or subtract two numbers if the exponents are the same; simply add or subtract the coefficients and keep the exponent the same. (Note: if the exponents are not the same, you must make one the same as the other before adding or subtracting)

Practice Problems 1. Write in scientific notation: a. 0.000467 b. 32000000

Practice Problems 2. Express 5.43 x 10-3 as a number.

Practice Problems 3. (4.215 x 10-2) + (0.032 x 10-2) =

Practice Problems 4. (8.97 x 104) - (0.262 x 104) =

Practice Problems 5. (4.5 x 10-14) x (5.2 x 103) = ?

Practice Problems 6. (6.1 x 105) ÷ (1.2 x 10-3) = ?

Answers: (1a) 4. 67 x 10-4; (1b) 3. 2 x 107 (2) 0. 00543 (3) 4 Answers: (1a) 4.67 x 10-4; (1b) 3.2 x 107 (2) 0.00543 (3) 4.247 x 10-2 (4) 8.71 x 104 (5) 2.3 x 10-10 (2 significant figures) (6) 5.1 x 108 (2 significant figures)