Fractions & Decimals
Convert 1/4 to a decimal.
0.25
What is |−7|?
7
What is 7²?
49
Which is less: −1.5 or −2/3?
-1.5
What is the smallest number set containing 0: natural, whole, integer, rational, or irrational?
Whole
Convert 7/8 to a decimal.
0.875
What is |−3/4|?
3/4 or 0.75
What is √121?
11
Order −√9, −0.8, and 0 from least to greatest.
−√9 (−3), −0.8, 0
What is the smallest number set containing −7?
Integer
Convert 2 3/4 to a decimal.
2.75
Which two numbers in {−8, 2.5, −2.5, 6} have the same absolute value?
2.5 and −2.5; both have absolute value 2.5.
Between which consecutive whole numbers does √50 lie? Use perfect squares.
Between 7 and 8, because 49 < 50 < 64.
Put <, =, or > between −3/4 and −0.72.
−3/4 < −0.72 because −0.75 < −0.72.
Is √16 rational or irrational? Explain.
Rational: √16 = 4, a natural number and therefore rational.
Convert 5/11 to a decimal. State whether it terminates or repeats.
0.454545...; it repeats (45 repeats).
Find both numbers x that satisfy |x| = 5.
−5 and 5
Name two whole numbers whose positive square roots lie between 7 and 8.
Any two whole numbers from 50 through 63, such as 50 and 60.
Order −√4, −1.8, −7/4, and 0.1 from least to greatest.
−√4 (−2), −1.8, −7/4 (−1.75), 0.1
Classify √10 as rational or irrational, and explain.
Irrational: 10 is not a perfect square, so √10 cannot be expressed as a ratio of integers.
Without a calculator, which is greater: 7/8 or 0.86? Show the comparison.
7/8 = 0.875, and 0.875 > 0.86; therefore 7/8 is greater.
Sam says |−9| = −9. Correct the claim and explain.
|−9| = 9 because −9 is 9 units from zero; distance is nonnegative.
Maya says √36 = 18 because 18 is half of 36. Correct her and explain the operation.
√36 = 6 because 6 × 6 = 36; a square root undoes squaring, not halves a number.
Order −1.5, 3/4, −2/3, √4, and 0.2 from least to greatest.
−1.5, −2/3, 0.2, 3/4, √4
Mystery: I am rational, between 0.4 and 0.5, and equivalent to a fraction with denominator 9. What am I?
4/9 = 0.444..., which is rational and between 0.4 and 0.5.