Scientific Notation

1. Scientific Notation Mrs Vass BJH

2. Scientific Notation • 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

3. 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

4. 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 inscientific notation as 5. 0 x 10 -3 .

5. 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

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

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

8. 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

9. 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

10. 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 5written in standard form is 674000

11. 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

12. 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 FACTORSwithout 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

13. 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.