Name:_______________________________
2.3 Comparing and Ordering Rational Numbers
To order decimals from least to greatest (Review):
1. Rewrite the given numbers in a column, lining up the decimal points one under each other.
2. Make them the same length: fill empty spaces with zeros OR
with the repeating pattern if you have repeating digits (bar notation) up to thousands.
3. Compare the whole numbers in front of the decimal points; order them from least to greatest.
4. If the numbers are equal, move one column to the right, compare digits in the tenths place. Put them in order.
5. If the digits are equal, move to the next column, compare digits in the hundredths place. Order them, etc.
6. Final answer must be given in the original form.
Order the following decimals from least to greatest:
1) 0.402, 0.42, 0.375, 1.2
Answer:
2)
�, 0.321, 2.52
�, 2.𝟓
0.3𝟐
3)
Answer:
Answer:
Compare the following rational numbers using >, <, or =
1) 10%
4)
2
3
4
1
5
2.75%
2) 0.5
5) 15%
3
5
1
5
�; 7.88; 8.01; 7.79
7.𝟖
3) 1.7
To order rational #s:
170%
1. Convert #s to decimals
2. Put them in order
6) 50%
0.05
3. Rewrite them in the
original form
Order the following numbers:
3
1
7) from least to greatest: 135%, 13.5, 8 , 3.9 × 102
8) from greatest to least: , 16.7%, 0.16, 3.2 × 10−3
5
9) from least to greatest: 0.42, 4.2%,
2
5
6
, 4.1 × 101
10) from greatest to least: 3
1
3
, 3.34, 300%, 4 × 10−3
Put the following in descending order:
1
11)
45%,
, 0.6, 1²
12)
13)
− , –10%, (–5)², – 0.6
2
3
4
4², 0.8, 50%, 0, 5.91 × 10−8
14) 5.91 × 10−8 ; 5.01 × 1010 ; 5.18 × 10−8 ; 8.45 × 10−9
Put the following numbers in ascending order:
15) 45%, 4.6 × 10−2 ,
1
, 0.045
2
1
16) 125%, 1.2 × 102 , 1 , 1.26
2
17) About 17% of kids will attend an overnight summer camp,
no summer camp at all. Which group of kids is the greatest?
11
50
will attend a day camp, and 0.59 will attend
18) In a recent year, Major League Baseball player Jack Wilson’s batting average was 0.308. Melvin Mora hit
safety 17 out of every 50 at-bats and Bobby Abreu hit safety 30.1% of the time. Find Mora’s and Abreu’s
batting averages and order all three averages from least to greatest.
Fractions
Decimals
– 0.25
Percent
7
5 10
Review
1
3
Scientific Notations
7%
8 x 10−2
13.2�
19) A submarine ascended from 56.8 meters under the sea level to 27.4 meters under the sea level. Find the
distance it moved between two positions. Use the “distance on the number line “formula.
20) Write number sentences represented on the following models
a) ____________________
b) ____________________
Calculate
21) 9 + (–15)(2)
22)
15+6
−7
c) ____________________
23) 2 · (−2)³
HOMEWORK 2.3
For the problems below, put the numbers in ascending order.
1)
0.23, 0.023 x 103 , 2.30%,
1
2)
5
0.017 x 103 , 1.7%, 0, 1.7 x 10−4 , 170
For the problems below, put the numbers in descending order.
1
1
3) –1.25, 1 , 1 , 4², 160
4
4) 8.01 x 102 , 5.45 x 10−1 ,
3
5) At Jeremy’s high school, about
3
16
1
2
, 3.79
of the students are in the band, 0.31 of high school students play at least
one sport, and 13% are in the drama club. List these types of activities from least to most popular.
6) You can express ________________ as a fraction by writing it as a fraction with a denominator of 100.
7) Rewrite 10−3 as a fraction and as a decimal.
8) Evaluate 54
9) There are 14 black pens out of 25 pens. What percent of the pens are black?
10) Write 0.00000000082 using scientific notation.
11) Which numbers are not written in scientific notation (more than one)? Why?
a) 5 x 10−1
b) 10.2 x 10−5
c) 5.73 x 10123
d) 0.8 x 105
e) 7.3 x 84
12) The Eagles lost a total of 54 yards over 9 plays. What is the average number of yards lost per play?