Repeating Decimals
Write the following as a simplified fraction:
0.77777...
7/9
Is the following rational or irrational? Be prepared to prove your answer.
sqrt(8)
Irrational: Not a perfect square and is approximately 2.83
sqrt(89)
is between what two whole numbers
9 and 10
Use the properties of exponents to write an equivalent expression using exponents:
4^10 ÷ 4^4 * 4^3
4^9
Write the following numbers in standard form:
0.000000001027
103900
1.027 * 10^(-9)
1.039 * 10^5
Blue Ticket Question
A trail at a nature park is divided into sections. During a hike, Maya walked
0.2\overline{38}
miles on the first section and
0.1\overline{4}
miles on the second section.
How far did Maya walk in all? Write your answer as a fraction in simplest form.
0.2\overline{38}=236/990=118/495
0.1\overline{4}=13/90
LCD 990 (236/990) + (143/990) =
379/990 miles
Write the following as a simplified fraction:
0.044444444...
2/45
Is the following rational or irrational? Be prepared to prove your answer.
0.743743743...
Rational: Can be turned into the fraction
743/999
sqrt(47)
is closest to what whole number
7
What is an equivalent expression that uses only positive exponents for
(3^6)^(−2)
1/(3^12)
(2.8 times 10^4) times (4 times 10^5)
Write the answer in scientific notation
1.12 times 10^10
Order the following values in descending order:
0.00482 times 10^(3) , 4 5/6 , 4.8\overline{3} , 97/20 , sqrt(23.5)
97/20 , sqrt(23.5) , 4 5/6 , 4.8\overline{3} , 0.00482 times 10^(3)
Write the following as a simplified fraction:
0.454545...
5/11
Is the following rational or irrational? Be prepared to prove your answer.
sqrt(36/64)
Rational:
sqrt(36)/sqrt(64)=6/8=3/4
sqrt(111)
is closest to what whole number
11
Evaluate the expression for x = 2 and y = 5
−4x^(−2) + 3y^0
2
DAILY DOUBLE
The average distance from Earth to the Sun is about
1.5 * 10^8
km. The average distance from Earth to the Moon is about
3.8 * 10^5
km. In standard form, ABOUT how many times greater is the distance from Earth to the Sun than the distance from Earth to the Moon?
(1.5 * 10^8)/(3.8 * 10^5) ≈ 0.4 * 10^3≈400
400 times greater
A park ranger is mapping hiking trails. The lengths are
sqrt{18}, sqrt(27), and sqrt(40)
miles. About how many miles are there altogether? Round each square root to the nearest tenth.
sqrt(18)≈4.2
sqrt(27)≈5.2
sqrt(40)≈6.3
4.2+5.2+6.3= 15.7 miles
Write the following as a simplified fraction:
0.2533333...
19/75
Blue Ticket Question
Is the following rational or irrational? Be prepared to prove your answer.
pi/(4pi)
Rational:
pi/(4pi)=1/4*pi/pi=1/4*1=1/4
Approximate
sqrt(55)
to the nearest tenth
7.4
Evaluate the expression for x = 2 and y = 5
2x^0y^(-2)
2/25
(4.1 times 10^4) + (2.6 times 10^6)
Write your answer in Scientific Notation
5.641 times 10^6
DAILY DOUBLE
((x^(-2)y^3)^2(x^4y^(-5)))/(x^(-1)y^2)
x/y
Write the following as a simplified fraction:
0.56121212...
463/825
DAILY DOUBLE
Is the following rational or irrational? Be prepared to prove your answer.
(15pi^2)/(3pi)
Irrational:
(15pi^2)/(3pi)=(15/3)*(pi^2/pi)=5*pi^(2-1)=5pi
Approximate
sqrt(70)
to the nearest hundredth
8.37
Use the laws of exponents to simplify the expression:
((x^3y^(-2))^2)/(x^4y^(-5)
x^2y
A wildlife reserve finds that there were
4.2 * 10^6
monarch butterflies at the beginning of the migration season. By the end, only
8.5 * 10^5
butterflies remained. How many monarch butterflies were lost during the migration season?
3.35 * 10^6
Blue Ticket Question
3/8 ÷ (-2/5) + 1/3
3/8 ÷ -2/5 = 3/8 * -5/2 = -15/16
-15/16 + 1/3 = -45/48 + 16/48 =
-29/48