Expressing numbers

by Osama M. Khaled last modified 2022-05-31T21:40:26+01:00

Quantities have two parts: the number and the unit. The number tells “how many.” It is important to be able to express numbers properly so that the quantities can be communicated properly.

Questions #: 7
Pass Score: 80.0%

Standard notation is the 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 306,000,000, 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 is an expression of a number using powers of 10. Powers of 10 are used to express numbers that have many zeros:

100  = 1
101  = 10
102  = 100 = 10 x 10
103  = 1,000 = 10 x 10 x 10
104  = 1,000 = 10 x 10 x 10 x 10


and so forth. The raised number to the right of the 10 indicating the number of factors of 10 in the original number is the exponent. Scientific notation is sometimes called exponential notation. The exponent’s value is equal to the number of zeros in the number expressed in standard notation.  Small numbers can also be expressed in scientific notation but with negative exponents:

10-1  = 0.1 = 1/10
10-2  = 0.01 = 1/100
10-3  = 0.001 = 1/1,000
10-4  = 0.0001 = 1/1,0000

 

    Standard notation does not expresses a number normally

    True
    False

    Scientific notation expresses a number as a coefficient times a power of ______.

    Missing

    The power of 10 is positive for numbers greater than 1 and negative for numbers between 0 and 1.

    True
    False

    Express 306,000 in scientific notation

    a) 3.06 × 105            b) 30.6 x 104    c) 306 x 103    d) 0.306 x 106

    a
    b
    c
    d

    Express 0.00884 in scientific notation

    a) 88.4 x 10-2      b) 8.84 × 10−3      c) 8.84 x 10-5      d) 8.84 x 10-1

    a
    b
    c
    d

    Express 2,760,000 in scientific notation

    a) 2.76 × 105      b) 2.76 × 104       c) 2.76 × 106       d) 2.76 × 107

    a
    b
    c
    d

    Express 0.000000559 in scientific notation

    a) 5.59 × 10−8       b) 5.59 × 10−7     c) 5.59 × 10−5       d) 5.59 × 10−6

    a
    b
    c
    d