Scientific Notation Mrs Vass BJH

Scientific Notation which is 6.7 x 1010 Definition: Scientific notation is a symbol that expresses any number as a power of ten multiplied by a number between 1 and 10 (including 1). Scientific notation allows you to work with very large numbers and very small numbers. A number like 5 000 000 000 would be 5.0 x 10 9 5 > 1 and < 10 and there are 9 places past where the new decimal place would be. Write the scientific notation for 67 000 000 000 which is 6.7 x 1010

Scientific Notation Which of the following numbers are in scientific notation? If it is not, explain why.  a.    3 x 106  b.   4.6 x 10-4  c.    0.2 x 108 d.   2.8 x 100 Answers A) is correct scientific notation as the decimal number is less than 10 and equal to or greater than 1. It is also written in a power of 10 B) is correct for the same reasons as A C) is not correct as the decimal number is less than 1 D) is not correct as the decimal is correct but it is not written in a power of 10 . If it was changed to 102 it would be correct

Scientific Notation How do we represent very small numbers in scientific notation? Recall that 0.005 = 5 x 1 or 5 x 1 1000 103 Therefore, armed with the above knowledge, our previous knowledge of negative exponents, and the definition for scientific notation, 0.005 is represented in scientific notation as 5. 0 x 10 -3 .

Scientific Notation The calculator only holds 7 digits. So if you have a number like 760 000 000 it would show it as 7.62 x 10 8 . If you have a positive exponent for 10, then the decimal place will move to the right and make the number bigger such as 3.45 x 105 = 345 000 If you have a negative exponent , the decimal point will move to the left and make the number smaller such as 3.45 x 10 –5 = . 0000345

Scientific Notation Trivia 106 million 109 billion 1012 trillion 1015 quadrillion 1018 quintillion 1021 sextillion 10100 googol

Scientific Notation Trivia The word googol was created in 1938 by the 11 year old nephew of the American mathematician Edward Kasner.

Operations with Scientific Notation Numbers can be written in standard form ( as a number) and scientific notation. You can do operations such as add, subtract , multiply and divide with scientific notation. Scientific notation allows you to solve more easily with very large or very small numbers. Remember that scientific notation is written in POWERS OF 10

Adding numbers with scientific notation: 1.4 x 10-3 + 2.3 x 10-3 If the power of 10 is the same then you can take out the power of 10 and then ADD the other two factors. For example: (1.4 + 2.3 ) x 10-3 3.7 x 10-3 written in standard form it would be 0.0037

Addition with Scientific Notation If the numbers are not in the same power of 10, then you might be able to rewrite the numbers so that they are in the same power of 10. 5.3 x 104 + 6.2 x 10 5 could be rewritten as 0.53 x 10 5 + 6.2 x 10 5 ( Now you can solve it as shown in previous slide) (0.53 + 6.2) x 10 5 6.73 x 10 5 written in standard form is 674000

Subtraction with Scientific Notation Subtraction is done the same way as addition. Take out the power of 10 and then subtract the other factors. 7.3 x 103 - 6.2 x 10 3 ( 7.3 – 6.2) x 10 3 1.1 x 10 3 written in standard form it is 1100

Multiplying in Scientific Notation When you multiply or divide with scientific notation , you will use your exponent laws. Remember , when we multiply powers with the same base , we add the exponents: (2.2 x 104 ) x ( 1.2 x 10 7) Remember that the Commutative Property allows us to rearrange the FACTORS without affecting the answer. SO : 2.2 x 1.2 x 104 x 10 7 2.64 x 10 (4 + 7) 2.64 x 10 11 or 264 000 000 000

Dividing with Scientific Notation 12.4 x 10 10 ÷ 3.2 x 10 6 and 3.875 x 10 (10 – 6) = 3.875 x 104 OR 38750 You need to divide the first factors and then apply the exponent laws to the powers of 10.