3. Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches.
pie, \/3, 2\/3, \/5

(a) Without using your calculator, approximate the decimal equivalent of each number to the nearest tenth.

(b) Order the ribbon sizes from least to greatest.

a) pi: 3.1

sqrt(3): 1.7

2sqrt(3): 3.5

sqrt(5): 2.2

b) least to greatest

sqrt(3)

sqrt(5)

pi

2sqrt(3)

Step-by-step explanation:

pi: 3.1

sqrt(3) is approximately 1.7

Because:

3 lies between two perfect squares, 1 and 4.

1 < 3 < 4

It's 2 and 1 units away from the ends

So a rough estimate would be:

1 + 2/3 = 1.66666667

To the nearest tenth, 1.7

2sqrt(3)

= sqrt(12) is approximately 3.5

Because:

12 lies between two perfect squares, 9 and 16

9 < 12 < 16

It's 3 and 4 units away from the ends

So a rough estimate would be:

3 + 3/7

Since 3/7 is almost ½

To the nearest tenth, 3.5

sqrt(5) is approximately 2.2

Because:

5 lies between two perfect squares, 4 and 9

4 < 3 < 9

It's 1 and 6 units away from the ends

So a rough estimate would be:

2 + 1/7

1/7 is slightly greater than 0.15

To the nearest tenth, 2.2

Least to greatest:

sqrt(3): 1.7

sqrt(5): 2.2

pi: 3.1

2sqrt(3): 3.5

sine

step-by-step explanation:

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