2.2.1: Preparation 2.2

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(1) The following problems have to do with multiplying and dividing by powers of 10. Look for patterns and ways to find the answers mentally without a calculator or writing the problem down. Check your answers with a calculator if you wish.

(a) 0.32 × 10

(b) 3.2 × 10

(d) 32 × 100

(e) 51,000 × 10,000

(f) 900 × 10⁴

(g) 1.3 × 10⁷

(h) 0.32 ÷ 10

(i) 3.2 ÷ 10

(j) 3,200,000 ÷ 10

(k) 5,500,000 ÷ 1,000

(l) 83,000,000 ÷ 10,000,000

(m) 67 ÷ 10⁴

(2) When you multiply 58,000,000,000 × 10,000, the calculator display will show: 5.8 E14. Which of the following represent(s) the same number as the number displayed on your calculator? There may be more than one correct answer.

(i) 5.8 × 14

(ii) 5.8 × 10¹⁴

(iii) 58 × 10¹⁴

(iv) 580,000,000,000,000

(v) 5,800,000,000,000,000

(3) The United States Department of Agriculture (USDA) publishes a “National Fruit and Vegetable Retail Report” every week.⁶ This shows the national average costs of fruits and vegetables from store advertisements. The weekly report on January 20, 2023 showed the following prices for Golden Delicious apples:

Commodity	Variety	Unit	Price (in US$)
Apples	Golden Delicious	per pound	1.29
Apples	Golden Delicious	3 lb bag	3.83

If these were the prices at your local grocery store, which would cost you more?

(i) Three pounds of Golden Delicious apples, bought per pound.

(ii) A 3-lb bag of Golden Delicious apples.

(iii) They would cost the same amount.

(4) The same report gave the prices for navel oranges:

Commodity	Variety	Unit	Price (in US$)
Oranges	Navel	each	0.90
Oranges	Navel	per pound	1.32
Oranges	Navel	4 lb bag	4.95

If these were the prices at your local grocery store, which purchase would cost the least?

(i) Four navel oranges.

(ii) Four pounds of navel oranges, bought per pound.

(iii) A 4-lb bag of navel oranges.

(iv) All three would cost the same amount.

After Preparation 2.2 (survey)

You should be able to do the following things for the next class. Rate how confident you are on a scale of 1–5 (1 = not confident and 5 = very confident).

Before beginning Unit 2.2, you should understand the concepts and demonstrate the skills listed below.

Skill or Concept: I can …	Rating from 1 to 5
calculate a unit rate.
make general sense of proportionality.

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⁶ http://www.ams.usda.gov/mnreports/fvwretail.pdf

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