Estimate and find percentages of whole number and decimal amounts.
Number Framework Stage 8
Using Number Properties
Problem: “Today the price of an ice cream in the country of Nuldova is $1.50. Prices are rising at a rate of a 100% per year. What will be the price of the same kind of ice cream in 20 years time?”
Discuss why 100% increase means doubling the price each year.
(Answer: 100% increase means the price is 200% of the original, that is, double.)
Discuss why prices are $1.50, $3, $6, $12 ... and how to enter this on a calculator.
(Answer: Enter 1.50 x 2 = = = = counting 20 equal signs, which gives $1,572,864.) Note: Some calculators require the user to go: 2 x 1.5 = = = = .... Carefully check which system your calculators use before attempting this problem.)
On some calculators, you can also use the yx button to get the answer.
(Answer: Enter 1.50 x 2 yx 20 = into the calculator.)
Example: In a country with inflation of 10% per year what will be the price of a $20,000 new car in 40 years time?
(Answer: 20 000 x (1.1)40 ≈ $905,185.)
Problem: “In a country where inflation is running wild at 56% per year, how long will it take for a $1 ice cream to cost $1,000,000?”
Discuss why entering 1.56 as a constant multiplier in a calculator is sensible. Get students to enter 1.56 x = = = = and count carefully.
(Answer: If, for example, the equals button has been pressed 4 times, the answer to 1.565 is in the display not 1.564. When 1.5631 has been entered, the display shows 970202.8566, and when 1.5632 has been entered, the display shows 1513516.456. So the cost reaches $1,000,000 in just over 30 years.)
Examples: For these rates of inflation, find out how long it will take a $1 ice cream to
cost $100,000,000: 99%, 87%, 300% , 50% , 1 000%
Understanding Number Properties:
If inflation is running at 10%, Gerry argues prices will double in 10 years. Explain why Gerry thinks this. Explain why Gerry is wrong. (Answer: Gerry says 10 x 10% = 100%, so the price increase by itself, that is to say doubles, in 10 years. But he is wrong. Adding 10% to, say, $1 gives a price of $1.10. For the next year, 10% is added to $1.10 not $1 to give $1.21. So the 10% added each year is being added t o an increasing amount every year, so prices will double in less than 10 years.)