Compare −π and −3.14 using < or > and explain.
−π < −3.14 because −3.14159… is slightly less.
Write the integer for ‘a cliff 275 meters above river level.’
275
Which is smaller: −2.71 or −2.7?
−2.71 is smaller.
Order from smallest to largest: 5/8, 0.61, 0.625, 0.6.
0.6, 5/8 = 0.625, 0.61, 0.625
Is √2/2 rational or irrational? Explain.
Irrational because √2 is irrational, and dividing by 2 keeps it irrational.
Write two irrational numbers between −1 and 0.
−√0.5, −π/4
Compare 1.41 and √2 using < or > and explain.
1.41 < √2 because √2 ≈ 1.414…
Write the integer for ‘a tunnel 1,275 meters underground.’
−1275
Which has greater absolute value: −99 or 100?
100 because 100 > 99.
Order from smallest to largest: −7, −7.1, −7.01.
−7.1, −7.01, −7
Is 0.444… rational or irrational? Explain.
Rational because it equals 4/9.
Write three rational numbers between 3/2 and 2.
1.6, 1.7, 1.8
Compare 0.29 and 2/7 using < or > and explain.
0.29 > 2/7 because 2/7 ≈ 0.2857.
Write the integer for ‘a hot air balloon 725 meters above the ground.’
725
Which is smaller: −√3 or −1.73?
−√3 < −1.73 because √3 ≈ 1.732.
Order from smallest to largest: −π, −3.15, −3.1.
−3.15, −π ≈ −3.1416, −3.1
Is 5.121212… rational or irrational? Explain.
Rational because it has a repeating decimal pattern.
Write two rational numbers between −10 and −9.
−9.25, −9.5
Compare 0.101 and 1/9 using < or > and explain.
0.101 < 1/9 because 1/9 ≈ 0.111…
Compare −45 and −32 using < or > and explain.
−45 < −32 because −45 is farther left on the number line.
Write the integer that represents ‘a research drone is flying 2,350 meters below sea level.’
−2350
Order from smallest to largest: 0, −17, 4, −3, 2.5.
−17, −3, 0, 2.5, 4
Write three rational numbers between 2/5 and 3/5.
0.45, 0.5, 0.55
Is √50 rational or irrational? Explain.
Irrational because √50 = √(25×2) = 5√2, and √2 is irrational.
