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A rational number is any whole number, fraction, mixed number or decimal, including their negative counterparts. An example of a rational number is 8.5. It is rational because it can be turned into a simple fraction of 8 ^{1}⁄_{2}.

8 ^{1}⁄_{2} = 8.5

This quiz will test how well you know the value of your decimal rational numbers. For each set of decimal rational numbers below determine if the first rational decimal is greater than (>), less than (<), equal to (=) or cannot be determined (?).

1.

.67 ___ .629

>

<

=

?

2.

2.34 ___ 2.44

>

<

=

?

2.34 = 2 ^{34}⁄_{100} and 2.44 = 2 ^{44}⁄_{100}. 2 ^{34}⁄_{100} is less than 2 ^{44}⁄_{100} so Answer (b) 2.34 < 2.44 is the correct answer

3.

.8 ___ .2

>

<

=

?

.8 = 8/10 and .2 = 2/10. 8/10 is greater than 2/10 so Answer (a) .8 > .2 is the correct answer

4.

106.1 ___ 106 ^{10}⁄_{100}

>

<

=

?

106.1 can be rewritten as 106 ^{1}⁄_{10}. 106 ^{10}⁄_{100} can then be simplified by dividing the numerator and the denominator or 10/100 by 10. So 10 ÷ 10 = 1 and 100 ÷ 10 = 10 giving you 1/10 or 106 ^{1}⁄_{10}. Answer (c) 106.1 = 106 ^{10}⁄_{100} is correct

5.

5/8 __ 15/24

>

<

=

?

5/8 cannot be simplified so it remains the same. 15/24 can be simplified by dividing the numerator and the denominator by 3. So 15 ÷ 3 = 5 and 24 ÷ 3 = 8 giving you 5/8. Answer (c) 5/8 = 15/24 is correct

6.

174.011 ___ 174.1

>

<

=

?

174.011 = 174 ^{11}⁄_{1000} and 174.1 = 174 ^{1}⁄_{10}. 174 ^{11}⁄_{1000} is less than 174 ^{1}⁄_{10} so Answer (b) 174.011 < 174.1 is the correct answer

7.

42.007 __

>

<

=

?

42.007 can be rewritten as 42 ^{7}⁄_{1000}; however, we do not have a second number to compare it to so we cannot make a determination of the value of this rational decimal number. Answer (d) is the correct answer

8.

10.05 ___ 10.07

>

<

=

?

10.05 = 10 ^{5}⁄_{100} and 10.07 = 10 ^{7}⁄_{100}. 10 ^{5}⁄_{100} is less than 10 ^{7}⁄_{100} so Answer (b) 10.05 < 10.07 is the correct answer

9.

16 ^{3}⁄_{4} __ 16.75

>

<

=

?

16.75 can be rewritten as 16 ^{75}⁄_{100}. ^{75}⁄_{100} can then be simplified by dividing the numerator and the denominator by 25. So 75 ÷ 25 = 3 and 100 ÷ 25 = 4 giving you 3/4 or 16 ^{3}⁄_{4} Answer (c) 16 ^{3}⁄_{4} = 16.75 is correct

10.

112.009 ___ 115.009

>

<

=

?

112.009 = 112 ^{9}⁄_{1000} and 115.009 = 115 ^{9}⁄_{1000}. 112 ^{9}⁄_{1000} is less than 115 ^{9}⁄_{1000} so Answer (b) 112.009 < 115.009 is the correct answer

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^{67}⁄_{100}and .629 =^{629}⁄_{1000}.^{67}⁄_{100}is greater than^{629}⁄_{1000}so Answer (a) .67 > .629 is the correct answer