Comparing & Ordering Real Numbers Review

Estimating Square Roots

100

Is the square root of 10 closer to 3 or 4?

It is closer to 3

200

Estimate the square root of 56 to the nearest integer.

≈7

300

Estimate the opposite (-) of the square root of 111 to the nearest integer.

≈-11

400

Estimate the square root of 165 to the nearest tenth.

≈12.8

500

Bradley wants to paint a square canvas to hang in his living room. If he wants the area of the canvas to be 250 square inches, what should the dimensions of the canvas be? Round your answer to the nearest hundredth.

≈15.81 inches by 15.81 inches

Identifying Rational & Irrational Numbers

100

Is the square root of 60 rational or irrational?

It is irrational. It is the square root of a non-perfect square.

200

Identify the rational numbers from the list:

-8, 42.765998734..... , 15, Pi, square root of 1024, 1.3333..., 5.3 x 10^-1

-8, 15, square root of 1024, 1.3333....., 5.3 x 10^-1

300

Identify the irrational numbers from the list:

0, square root of 55, -29, 0.525252..., square root of 225

square root of 55

400

If 0.333333.... is a ration number, write it as a ratio of two integers.

1/3

500

Martin says that 0.166666.... is an irrational number because it cannot be written as a fraction. Do you agree with Martin? Show proof.

I disagree with Martin because 0.166666... = 1/6

Comparing Real Numbers

100

Which is greater?

-2.3 or the square root of 116

-2.3 < the square root of 116

200

Which is greater?

The square root of 27 or 5

The square root of 27 > 5

300

Which is greater?

0.3679832... or 0.4

0.3679832... < 0.4

400

Which is greater?

1.24 x 10² or 114

1.24 x 10² > 114

500

Which is greater?

The opposite of the square root of 42 or -6.6

The opposite of the square root of 42 > -6.6

Ordering Real Numbers

100

Put the numbers in order from least to greatest.

 7, the square root of 45, .92, -4, 9/2

-4, .92, 9/2, the square root of 45, 7

200

Put the numbers in order from least to greatest.

5/3, -4.7, the square root of 37, 4

-4.7, 5/3, 4, the square root of 37

300

Put the numbers in order from least to greatest.

-6, 4.333333.... , -2.8, 12/3

-6, -2.8, 12/3, 4.3¯

400

Put the following numbers in order from least to greatest.

12.5, -16/25, 1.59 x 10^-8, -1.5

-1.5, -16/25, 1.59 x 10^-8, 12.5

500

Put the following values in order from greatest to least.

2/33, 7.854 x 10⁹, 0/6, 7.86 x 10⁹, 7.82 x 10^-2

7.86 x 10⁹ , 7.854 x 10⁹ , 7.82 x 10^-2, 2/33, 0/6