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SAT Math : Decimals

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Example Questions

Example Question #361 : Arithmetic

Numberline 1

In the above number line, which point comes closest to $\frac{18}{29}$ ?

Possible Answers:

Correct answer:

Explanation:

Divide numerator 18 by denominator 29 to find the decimal equivalent of the fraction $\frac{18}{29}$ :

Division

The result is slightly higher than 0.62 - the point on the number line.

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Example Question #4 : Decimals

Write 0.45 as a fraction.

Possible Answers:

$\frac{3}{4}$

$\frac{2}{5}$

$\frac{5}{9}$

$\frac{9}{20}$

$\frac{11}{20}$

Correct answer:

$\frac{9}{20}$

Explanation:

.45 is equivalent to 45 out of 100, or $\frac{45}{100}$ .

Divide both the numerator and denominator by 5 to simplify the fraction:

$\frac{9}{20}$

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Example Question #12 : Decimals With Fractions

A tub of food contains 0.5 pounds of vegetables, 1.75 pounds of lard, and pounds of sausage. What is its total weight as an improper fraction?

Possible Answers:

$\frac{18}{4}$

$\frac{91}{8}$

$\frac{17}{4}$

$\frac{83}{4}$

$\frac{69}{4}$

Correct answer:

$\frac{69}{4}$

Explanation:

To begin with, it is easiest just to add these decimals together using your calculator:

0.5+1.75+15=17.25

Now, this is the same thing as:

17 + 0.25

We can rewrite this:

$17 + \frac{1}{4}$

To find this, you need to give the two numbers a common denominator:

$17 + \frac{1}{4} = \frac{68}{4}+\frac{1}{4}=\frac{69}{4}$

This is your answer.

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Example Question #13 : Decimals With Fractions

What is the fractional equivalent of 0.33 ?

Possible Answers:

$\frac{33}{100}$

$\frac{1}{3}$

$\frac{333}{1000}$

$\frac{3}{10}$

Correct answer:

$\frac{33}{100}$

Explanation:

In decimal form 0.33 is said 33 hundredths.

This is equal to

$\frac{33}{100}$ .

This fraction cannot be reduced any further therefore it is in its final answer form.

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Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

Convert the decimal to fraction form and reduce it to its simplest form.

0.825

Possible Answers:

$\frac{825}{1000}$

$\frac{33}{40}$

$\frac{13}{25}$

$\frac{165}{200}$

$\frac{21}{55}$

Correct answer:

$\frac{33}{40}$

Explanation:

In order to convert 0.825 to a fraction, you would first begin with $\frac{825}{1000}$ , because the decimal literally reads 825 thousandths. You can reduce by a few times or just begin by dividing both numbers by to get $\frac{33}{40}$ .

$\frac{825}{1000}=\frac{165}{200}=\frac{33}{40}$

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Example Question #21 : Decimals

If all real values of $x$ lie between 0 and 1, which of the following is always greater than 1?

Possible Answers:

$x^{2}$

$\frac{x}{10}$

$x^{4}$

$x+1$

$5x^{2}$

Correct answer:

$x+1$

Explanation:

If $x$ is greater than 0, then adding 1 to $x$ will make it greater than 1. Taking a number between 0 and 1 to a power results in a smaller number.

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Example Question #22 : Decimals

Evaluate:

0.08²

Possible Answers:

0.0064

0.64

0.00064

0.064

Correct answer:

0.0064

Explanation:

0.08 * 0.08

First square 8:

8 * 8 = 64

Then move the decimal four places to the left:

0.0064

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Example Question #1 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

$\sqrt{.00081}=$

Possible Answers:

0.9

0.028

0.009

0.09

Correct answer:

0.028

Explanation:

The easiest way to find the square root of a fraction is to convert it into scientific notation.

$\dpi{100} \small .00081 = 8.1 \times 10^{-4}$

The key is that the exponent in scientific notation has to be even for a square root because the square root of an exponent is diving it by two. The square root of 9 is 3, so the square root of 8.1 is a little bit less than 3, around 2.8

$\dpi{100} \small \sqrt{8.1 \times 10^{-4}} \approx 2.8 \times 10^{-2} \approx 0.028$

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Example Question #2 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

$\small \sqrt{0.0049}$

Possible Answers:

$\small 0.022$

$\small 0.07$

$\small 0.7$

$\small 0.007$

Correct answer:

$\small 0.07$

Explanation:

To find the square root of this decimal we convert it into scientific notation.

$\small 0.0049 = 49 \cdot10^{-4}$

Because $\small 10^{-4}$ has an even exponent, we can divide the exponenet by 2 to get its square root.

$\small \sqrt{0.0049} = \sqrt{49}\cdot\sqrt{10^{-4}} = 7\cdot10^{-2} = 0.07$

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Example Question #2 : Basic Squaring / Square Roots

Find the square root of the following decimal:

$\small \sqrt{0.025}$

Possible Answers:

$\small 0.005$

$\small 0.625$

$\small 0.158$

$\small 0.05$

Correct answer:

$\small 0.158$

Explanation:

This problem can be solve more easily by rewriting the decimal into scientific notation.

$\small 0.025 = 2.5 \times 10^{-2}$

Because $\small 10^{-2}$ has an even exponent, we can take the square root of it by dividing it by 2. The square root of 4 is 2, and the square root of 1 is 1, so the square root of 2.5 is less than 2 and greater than 1.

$\small \sqrt{0.025} = \sqrt{2.5}\times \sqrt{10^{-2}} = 1.58\times 10^{-1} = 0.158$

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SAT Math : Decimals

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #361 : Arithmetic

Example Question #4 : Decimals

Example Question #12 : Decimals With Fractions

Example Question #13 : Decimals With Fractions

Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

Example Question #21 : Decimals

Example Question #22 : Decimals

Example Question #1 : How To Find The Square Root Of A Decimal

Example Question #2 : How To Find The Square Root Of A Decimal

Example Question #2 : Basic Squaring / Square Roots

All SAT Math Resources

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