Repeating Decimals as Fractions
Rewrite
0.overline7
as a fraction.
7/9
1.5
is a rational number. Why?
It is a terminating decimal which is a rational number.
What two consecutive whole numbers does
sqrt(52)
fall between?
7 and 8
A cube-shaped sculpture has a volume of 64 cubic feet. What is the length of each edge of the cube?
4 feet
Solve the equation
a^2=1
a=1 and -1
Rewrite
0.overline93
as a fraction.
31/33
Is
pi/3
rational or irrational?
It is irrational because pi is a decimal that goes on forever with no consistent pattern.
Approximate
sqrt(14)
to the nearest tenth.
3.7
The area of a placemat is 100 square inches. What is the length of each side?
10 inches
Solve the equation
v^3=216
v=3
Rewrite
1.overline56
as a fraction.
1 56/99
sqrt(115)
is irrational. Why?
It is irrational because 115 is not a perfect square, so when you take the
sqrt(115)
you get a decimal that goes on forever with no pattern.
Compare
16/11
and
sqrt(3)
sqrt3 > 16/11
or
16/11 < sqrt3
because
sqrt3=1.7320508...
and
16/11=1.overline45
Would you classify the number 64 as a perfect square, perfect cube, both, or neither?
Both because
sqrt64=8
and
root(3)(64)=4
Solve
root(3)8
2
Rewrite
0.3overline12
as a fraction.
103/330
4.545545554...
is rational. True or False?
False because the decimal goes on forever with NO consistent repetitive pattern.
It would be rational if it was
4.54545454...
Put the real numbers in ascending order:
7.overline2, sqrt52, 7 2/7
sqrt52, 7.overline2, 7 2/7
Ty wants to build a square sandbox with an area of 121 square feet. What is the total length of wood Ty needs to make the sides of the sandbox?
One side=11 inches, so 11+11+11+11=44 inches of wood to make the sides of the sandbox.
Solve
sqrt7
sqrt7
Rewrite
5.2overline97
as a fraction.
5 59/198
Is
195
a perfect square, perfect cube, neither, or both?
It is neither because
sqrt(195)=13.96424004...
and
root(3)(195)=5.798889997...
. If the square or cube root is not a whole number, then it is irrational.
Compare
82/9
and
9.overline12
82/9<9.overline12
or
9.overline12>82/9
because
9.overline12=9.1212121212....
and
82/9=9.111111111....
The area of a baseball infield is 8100 square feet. If a player runs around all the bases, how far did he travel?
One side of the diamond=90 feet, so 90+90+90+90=360 feet around the bases.
Solve the equation
m^2=12
m=sqrt14 and -sqrt14