SCIENTIFIC NOTATION A QUICK WAY TO WRITE REALLY

SCIENTIFIC NOTATION A QUICK WAY TO WRITE REALLY, REALLY BIG OR REALLY, REALLY SMALL NUMBERS.

Mathematicians are Lazy!!! They decided that by using powers of 10, they can create short versions of long numbers.

Rules for Scientific Notation To be in proper scientific notation the number must be written with * a number between 1 and 10 * and multiplied by a power of ten 23 X 105 is not in proper scientific notation. Why?

4. 5 x 103 The number 4, 500 is written in scientific notation as ________. The coefficient is _____. 4. 5 The coefficient must be a number greater than or equal to 1 and smaller than 10. The power of 10 or exponent in this example is ______. 3 The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4, 500.

If a number is greater than 10, the exponent will be positive _______ and is equal to the number of places the decimal must be moved to left the ____ to write the number in scientific notation.

If a number is less than 10, the exponent will be negative _______ and is equal to the number of places the decimal must be moved to right the ____ to write the number in scientific notation.

To write a number in scientific notation: 1. Move the decimal to the right of the first non-zero number. 2. Count how many places the decimal had to be moved. 3. If the decimal had to be moved to the right, the exponent is negative. 4. If the decimal had to be moved to the left, the exponent is positive.

Soooo 137, 000 can be rewritten as 1. 37 X 8 10

Now You Try Using scientific notation, rewrite the following numbers. 347, 000. 3. 47 X 105 902, 000. 9. 02 X 108 61, 400. 6. 14 X 104

Convert these: 1. 23 X 105 123, 000 6 6. 806 X 10 6, 806, 000

Try These 4, 000 4 X 103 2. 48 X 103 2, 480 6. 123 X 106 6, 123, 000 306, 000 3. 06 X 108

In the United States, 15, 000 households use private wells for their water supply. Write this number in scientific notation. 1. 5 X 107

• The U. S. has a total of 1. 2916 X 107 acres of land reserved for state parks. Write this in standard form. 12, 916, 000 acres

Why does a Negative Exponent give us a small number? 10000 = 10 x 10 = 104 1000 = 10 x 10 = 103 2 100 = 10 x 10 = 10 1 = 100 Do you see a pattern?

Sooooo = 10 -1 = = 10 -2 = = 10 -3 = = -4 10

Your Turn Using Scientific Notation, rewrite the following numbers. 0. 000882 8. 82 X 10 -4 0. 00000059 5. 9 X 10 -7 0. 00004 4 X 10 -5

More Examples 1) 0. 0004 2) 3) 4) 5) 4 X 10 -4 1. 248 X 10 -6. 000001248 6. 123 X 10 -5. 00006123 0. 00000306 3. 06 X 10 -6 0. 000892 8. 92 X 10 -4

The nucleus of a human cell is about 7 X 10 -6 meters in diameter. What is the length in standard notation? . 000007

A ribosome, another part of a cell, is about 0. 00003 of a meter in diameter. Write the length in scientific notation. 3 X 10 -9

Using Scientific Notation in Multiplication, Division, Addition and Subtraction Scientists must be able to use very large and very small numbers in mathematical calculations. As a student in this class, you will have to be able to multiply, divide, add and subtract numbers that are written in scientific notation. Here are the rules.

Multiplication When multiplying numbers written in scientific notation…. . multiply the first factors and add the exponents. Sample Problem: Multiply (3. 2 x 10 -3) (2. 1 x 105) Solution: Multiply 3. 2 x 2. 1. Add the exponents -3 + 5 Answer: 6. 7 x 102

Division Divide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator. Sample Problem: Divide (6. 4 x 106) by (1. 7 x 102) Solution: Divide 6. 4 by 1. 7. Subtract the exponents 6 - 2 Answer: 3. 8 x 104

Addition and Subtraction To add or subtract numbers written in scientific notation, you must…. express them with the same power of ten. Sample Problem: Add (5. 8 x 103) and (2. 16 x 104) Solution: Since the two numbers are not expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other. 5. 8 x 103 =. 58 x 104 so. 58 x 104 + 2. 16 x 104 =? Answer: 2. 74 x 104