Name: ___________________________ Per. _____Ch1 A: Compare and order real number
A1.2.A Know the relationship between real numbers and the number line,
and compare and order real numbers with and without the number line.
Study Notes: When ordering numbers, always be sure which order:
Greatest to least: 10,
,
Least to greatest: 99,
2, 1,
1
, 1,
2
1
,  99
2
2,  , 10
Strategy: The fastest way is to use your calculator and convert all numbers to decimal approximations,
  3.14,
then order the numbers.

2  1.4,
1
 0.5
2
Scientific notation is a way to write very large or very small numbers.
The base number is always written as one place followed by a decimal
1.32 x 105 and not as 132 x 103
3.89 x 105 is equal to 389,000
3.89 x 10-5 is equal to 0.0000389
Move the decimal 5 places to the right
Move the decimal 5 places to the left.
9  3 because 32  9
8  2 because 23  8

Radicals:

Fractions: To convert a fraction to a decimal, divide the top by the bottom.
3
Examples
Practice
#1 Order the following from greatest to least.
37
82, 3 , 8.9, 8,
, 9.3x100
4
#1 Order the following from
greatest to least.
3,  , 3.6,
Solution: Find decimal
82  9.05, 3  9.42,
approximations:
37
 9.25, 9.3x100  9.3
4
8, 8.9, 9.05, 9.25, 9.3, 9.42
37
8, 8.9, 82,
, 9.3x100 , 3
4
14
, 3.7 x 10 2 , 23
4
Answer:
#2 A star’s color gives an indication of temperature and age. The
chart shows four types of stars and the lowest temperature of
each type. List the temperature in order from least to
#2 Scientific notation is used to
greatest.
measure the mass of very
large or very small objects.
Type Lowest Temperature
Color
Order the following masses
A
Blue-white
1.35 x 104
from least to greatest.
4
B
Blue
2.08 x 10
G
P
9.0 x 103
4.5 x 10 4
1.67 x 1027 kg
3.30 x 1023 kg
Yellow
Blue
Solution: Smallest number is 9.0 x 10  900
All the other numbers have a 104
3
9.0 x 103
1.35 x 104
2.08 x 104
4.5 x 10 4
9.11 x 1031 kg
4.87 x 1024 kg
Answer: