2.1 Expressing numbers book notes

Express these numbers in scientific notation. 1. 306,000 2. 0.00884 3. 2,760,000 4. 0.000000559

1. 3.06 × 10^5. The number 306,000 is 3.06 times 100,000, or 3.06 times 105. 2. 8.84 × 10^−3 The number 0.00884 is 8.84 times 1/1,000, which is 8.84 times 10−3. 3. 2.76 × 10^6. The number 2,760,000 is 2.76 times 1,000,000, which is the same as 2.76 times 106. In scientific notation, the number is written as 2.76 × 106. Note that we omit the zeros at the end of the original number. 4. 5.59 × 10^−7 The number 0.000000559 is 5.59 times 1/10,000,000, which is 5.59 times 10−7.

Small numbers can also be expressed in scientific notation but with negative exponents: 0.1 0.01 0.001 0.0001

10^-1 10^-2 10^-3 10^-4

Powers of 10 are used to express numbers that have many zeros: 1 10 100 1,000 10,000

10^0 10^1 10^2 10^3 10^4

write 0.000411 in scientific notation

4.11 x 10^-4 0.000411 = 4.11 x 1/10000 = 4.11 x 10^-4 (smaller # = NEGATIVE EXPONENT)

write 79,345 in scientific notation

7.9345 x 10^4 79345 = 7.9345 x 10000 = 7.9345 x 10^4

Standard notation

A straightforward expression of a number. Numbers such as 17, 101.5, and 0.00446 are expressed in standard notation. For relatively small numbers, standard notation is fine. However, for very large numbers, such as 324,000,000, or for very small numbers, such as 0.000000419, standard notation can be cumbersome because of the number of zeros needed to place nonzero numbers in the proper position.

Scientific Notation

An expression of a number using powers of 10. (sometimes called exponential notation.) A number is expressed in scientific notation by writing the first nonzero digit, then a decimal point, and then the rest of the digits.

Coefficient

The part of a number in scientific notation that is multiplied by a power of 10.

Exponent

The raised number to the right of a 10 indicating the number of factors of 10 in the original number. The exponent's value is equal to the number of zeros in the number expressed in standard notation.

A negative exponent on 10 does not mean that the number is negative. It means that the number is _________________ ______ and _______.

between 0 and 1

Key Takeaways: Scientific notation expresses a number as a _________ times a _______ of _______.

coefficient; power of 10

Key Takeaways: Standard notation expresses a number _________.

normally

Quantities have two parts: the _______ and the _______

number; unit

Key Takeaways: The power of 10 is _______ for numbers greater than 1 and ________ for numbers between 0 and 1.

positive; negative

It is important to be able to express numbers properly so that the ___________________________________________________________________________.

quantities can be communicated properly