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SAT Math : Arithmetic

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Example Questions

Example Question #431 : Arithmetic

Which of the following is the greatest in value?

Possible Answers:

$\frac{9}{4}$

2.5

$\frac{5}{2}$

$\frac{8}{3}$

2.556

Correct answer:

$\frac{8}{3}$

Explanation:

Turn the fractions into decimals to easily compare them. You can do this quickly on your calculator.

$\dpi{100} \small \frac{8}{3}$ is approximately 2.667, so this is the largest number.

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Example Question #432 : Arithmetic

Which of these decimals has the least value?

Possible Answers:

0.00012

0.001

1.0001000

0.0001000

0.10000001

Correct answer:

0.0001000

Explanation:

Trailing zeros at the end of a decimal do not increase or decrease the value of a given decimal. However, zeros that appear after the decimal point and precede a non-zero number decrease the value of the number.

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Example Question #3 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Put the following in order of least to greatest:

$0.28, \frac{6}{19}, \frac{29}{104}, 0.27,\frac{7}{26}$

Possible Answers:

$0.27, \frac{7}{26}, \frac{29}{104}, 0.28, \frac{6}{19}$

$\frac{7}{26}, 0.27, 0.28, \frac{29}{104}, \frac{6}{19}$

None of the other answers

$\frac{7}{26}, \frac{29}{104}, 0.27, 0.28, \frac{6}{19}$

$0.27, 0.28, \frac{7}{26}, \frac{29}{104}, \frac{6}{19}$

Correct answer:

None of the other answers

Explanation:

Begin by converting each fraction into a decimal:

$\frac{6}{19}\approx 0.3157$

$\frac{29}{104}\approx0.2788$

$\frac{7}{26}\approx0.269$

Now we can put the decimals in order:

0.269, 0.27, 0.2788, 0.28, 0.3157

or:

$\frac{7}{26}, 0.27, \frac{29}{104}, 0.28, \frac{6}{19}$

No answer choice matches this order, so our answer is "None of the other answers"

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Example Question #5 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Order the decimals from least to greatest. a=[0.2, 0.03,-2,-2.2]

Possible Answers:

a=[0.03,0.2,-2,-2.2]

a=[-2,-2.2,0.2, 0.03]

a=[-2.2,-2, 0.03,0.2]

a=[-2,-2.2, 0.03,0.2]

a=[-2,-2.2,0.2,0.03]

Correct answer:

a=[-2.2,-2, 0.03,0.2]

Explanation:

The higher negative numbers will be the least numbers.

Start with the negative numbers first.

-2.2 , -2

The smaller of the two positive decimals is 0.03 .

Order from least to greatest.

The answer is: a=[-2.2,-2, 0.03,0.2]

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Example Question #1 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Which decimal is the greatest?

Possible Answers:

$0.1^{2}$

$\frac{1}{0.1}$

0.1*2

$\frac{0.1}{2}$

0.1

Correct answer:

$\frac{1}{0.1}$

Explanation:

When evaluating, we look at each choice.

0.1^2=0.01

$\frac{1}{0.1}=10$

0.1=0.1

0.1*2=0.2

$\frac{0.1}{2}=0.05$

It seems like when dividing with a decimal, our value is greater. Therefore $\frac{1}{0.1}$ is our answer.

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Example Question #6 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Which is the smallest?

Possible Answers:

$\frac{5}{0.245}$

0.245*3

0.245+0.245+0.00000003

0.245^2

$\frac{0.245}{5}$

Correct answer:

$\frac{0.245}{5}$

Explanation:

When evaluating, we look at each choice.

.245^2=0.060025

$\frac{.245}{5}=.049$

.245*3=.735

.245+.245+.00000003=.49000003

$\frac{5}{.245}=20.41$

Our answer is $\frac{.245}{5}$ being the smallest.

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Example Question #7 : How To Order Decimals From Least To Greatest Or From Greatest To Least

If is from 0<x<1 which is the greatest?

Possible Answers:

x^2

x^3

x-5

Correct answer:

Explanation:

The numbers are from to . This means the values are decimals and will be small if raised to any power but greater when multiplied or added.

Ex: 0.1^3=0.001 vs 0.1^2=0.01 vs 2*0.1=0.2

Our answer is going to be .

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Example Question #11 : How To Order Decimals From Least To Greatest Or From Greatest To Least

If is from -1<x<0 , which of the following is the greatest?

Possible Answers:

x^3

x^2

x-5

Correct answer:

x^2

Explanation:

Since the range is from to , we have negative decimals. We need to see if any operations will generate positive decimals. Only x^2 does that as two negatives becomes positive when multiplied.

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Example Question #12 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Rank from smallest to greatest.

0.25, 0.54, 0.48, 0.35, 0.21

Possible Answers:

0.48, 0.54, 0.24, 0.21, 0.35

0.25, 0.54, 0.48, 0.35, 0.21

0.21, 0.24, 0.35, 0.48, 0.54

0.54. 0.48, 0.35, 0.24, 0.21

0.35, 0.21, 0.24, 0.48, 0.54

Correct answer:

0.21, 0.24, 0.35, 0.48, 0.54

Explanation:

To rank, we check the tenths digit. 0.21, 0.24 are the smallest in the set.

Next, we look at the hundredths digit. is greater than , so the rank is 0.21, 0.24 .

Since the next three numbers have differnt tenths digit, we just put in numerical order.

Final answer should be

0.21, 0.24, 0.35, 0.48, 0.54 .

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Example Question #11 : Ordering

Which decimal is the GREATEST?

Possible Answers:

0.500000000

0.5

0.499999

0.500001

0.49999

Correct answer:

0.500001

Explanation:

The tenths digits are different. 0.5 , 0.500000000 , and 0.500001 are clearly bigger than the other two.

So now, we compare the remaining decimals.

0.5 , 0.500000000 are exacty the same decimal with just more zeroes.

0.500001 is clearly the biggest as it is 0.000001 much bigger.

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SAT Math : Arithmetic

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #431 : Arithmetic

Example Question #432 : Arithmetic

Example Question #3 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Example Question #5 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Example Question #1 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Example Question #6 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Example Question #7 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Example Question #11 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Example Question #12 : How To Order Decimals From Least To Greatest Or From Greatest To Least

Example Question #11 : Ordering

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