Infinite Limits and Density
Are there any numbers between 2 and 3? Explain
Infinitely many numbers.
Convert 1/2 into a decimal and a percentage.
Decimal: 0.5
Percentage: 50%
Convert 18% into a decimal.
0.18
Evaluate: 2⁴
16
Express 15:3 in lowest terms.
5:1
Write 3 numbers between 2 and 3.
2.2, 2.5, 2.9 (any valid decimals between 2 and 3)
Calculate: 1/4 + 1/4
1/2
Convert 18 months into years.
1.5 years
Evaluate: (−3)⁴
81
A 4-hour snowstorm produces 24 cm of snow. What is the unit rate per hour?
6 cm/hour
Is the set {6, 7, 8, 9, …} finite or infinite? Explain.
It is infinite because it keeps increasing and never ends
What is 25% of 200
50
A bank offers 3% simple interest. If you invest $1000 for 2 years, how much interest do you earn?
Evaluate using order of operations: 2³ + 9 ÷ (−3)
5
Solve the proportion: 5:x = 40:48
6
Why is there no “last number” between 2 and 3?
Because between any two numbers you can always find another number, so the process never ends.
A jacket costs $90 and is on sale for 30% off. What is the new price?
$63
Jaryl deposits $2000 at 1.5% simple interest for 3 years. How much money will he have in total?
Evaluate: (−4)³ + 2 × (7 − 4)⁴
98
A paint mix uses white to blue in a ratio of 2:3. How many white cans are needed for 15 blue cans?
10
The sequence 8.1, 8.01, 8.001, 8.0001, … approaches what value? Explain what this represents.
It approaches 8. It represents a limit, where the values get closer and closer to 8 but never go past the pattern.
A bacteria population starts at 50 and grows by 20% every 5 minutes. What is the population after 15 minutes?
After 5 min = 60
After 10 min = 72
After 15 min = 86.4
Which investment earns more interest?
Option A: $3000 at 3% for 18 months
Option B: $3000 at 2% for 36 months
Option A = $135
Option B = $180
Option B earns more interest.
Which expression equals the correct value: (−2)⁵ or −2⁵?
Both equal −32
A map scale is 1 cm : 2.5 km. If the distance is 24 cm, what is the real distance?
60 km