# SAT Math : Decimals

## Example Questions

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

0.3 < 1/3

4 > √17

1/1/8

–|–6| = 6

Which of the above statements is true?

–|–6| = 6

0.3 < 1/3

1/< 1/8

4 > √17

0.3 < 1/3

Explanation:

The best approach to this equation is to evaluate each of the equations and inequalities.  The absolute value of –6 is 6, but the opposite of that value indicated by the “–“ is –6, which does not equal 6.

1/2 is 0.5, while 1/8 is 0.125 so 0.5 > 0.125.

√17 has to be slightly more than the √16, which equals 4, so“>” should be “<”.

Finally, the fraction 1/3 has repeating 3s which makes it larger than 3/10 so it is true.

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

How much less is  than ?

is greater than .

Explanation:

### Example Question #1 : Decimals

The ogre under the bridge eats  of a pizza and then throws the rest of the pizza to the rats. The rats eat  of what is left. What fraction of the pizza is left when the rats are done?

Explanation:

1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.

1/4 * 1/5 = 1/20 = 5%

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

Which of the following numbers is between 1/5 and 1/6?

0.16

0.25

0.22

0.19

0.13

0.19

Explanation:

Long division shows that 1/5 = 0.20 and 1/6 = 0.16666...  0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.

### Example Question #1 : Decimals

Trevor, James, and Will were each given a candy bar. Trevor ate 7/12 of his and Will ate 20% of his. If James ate more than Will and less than Trevor, what amount could James have eaten?

2/7

9/15

3/5

8/9

1/10

2/7

Explanation:

Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20  and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.

### Example Question #3 : Decimals

0.05

0.04

0.01

0.10

0.07

0.07

Explanation:

Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.

### Example Question #1 : Decimals

Approximate the fraction to decimal and round to three decimal places:

Explanation:

In order to estimate this fraction, set up a proportion equal to where the denominator is something of 100 parts.

Cross multiply.

Divide seven on both sides.

Rewrite the proportion.

To find the decimal, simply move the decimal place of the numerator back two spaces, and the denominator two spaces back as well.

### Example Question #1 : Decimals With Fractions

Find the decimal equivalent to the following fraction:

Explanation:

To find the decimal equivalent of a fraction, divide the numerator by the denominator. Because the number in the numerator is smaller than the number in the denominator, you have to place the decimal point after it and add zeros. Then complete long division. In many cases, the decimal will not end, so the best thing to do is divide until you get four decimal places, then round accordingly. For this question that will look like this:

To perform long division make sure the value in the numerator is within the division symbol.

From here, because the inside value is less than the outside value make sure to add a decimal and a zero.

Now, evaluate how many times 7 goes into 50. Since seven times seven is 49 and that is the closest values to 50 without going over, that is the first value in the decimal. From here subtract 49 from 50.

Now, evaluate how many times 7 goes into 10. In this case it is only once. Multiply one by seven and subtract this product from 10.

Now, evaluate how many times seven goes into 30. Since seven times four is 28, this is the closest value to 30 without exceeding it and thus is the value we choose.

Since all the answer choices stop at three digits we are done.

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

Find the decimal equivalent of the fraction:

Explanation:

To find the decimal equivalent of a fraction, divide the numerator by the denominator. Because the number in the numerator is smaller than the number in the denominator, you have to place the decimal point after it and add zeros. Then complete long division. In many cases, the decimal will not end, so the best thing to do is divide until you get four decimal places, then round accordingly. For this question that will look like this:

To perform long division make sure the value in the numerator is in the division symbol.

From here, we need to add a decimal point and zero because the inside value is less than the outside value.

Now, evaluate how many times 16 goes into 150. Since 16 times 9 is 144 and that is the closest value to 150 without going over, that is the first value in the decimal. From here subtract 144 from 150.

Now, evaluate how many times 16 goes into 60. Since 3 times 16 is 48, subtract that number from 60.

Now, evaluate how many times 16 goes into 120. Since 16 times 7 is is 112, this is the closest value to 120 without exceeding it which means it the value we need to choose.

Since all the answer choices stop at three digits we are done.

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

Find the decimal equivalent of the fraction:

Explanation:

To find the decimal equivalent of a fraction, divide the numerator by the denominator. Because the number in the numerator is smaller than the number in the denominator, you have to place the decimal point after it and add zeros. Then complete long division. In many cases, the decimal will not end, so the best thing to do is divide until you get four decimal places, then round accordingly. For this question that will look like this:

To perform long division make sure the value in the numerator is in the division symbol.

From here, we need to add a decimal point and zero because the inside value is less than the outside value.

Now, evaluate how many times 8 goes into 10. In this case, it is only once, so multiply 1 by 8 to get 8. From here subtract 8 from 10.

Now, evaluate how many times 8 goes into 20. Since 2 times 8 is 16, subtract that number from 20.

Now, evaluate how many times 8 goes into 40. Since 8 times 5 is is 40, this is the value we need to choose.

Since our final answer after subtracting is zero, we are done.