Decimals - ACT Math
Card 0 of 747
What is 
?
What is
You can solve this on your calculator, or think about it as a fraction 
to make the problem easier to do by hand. 
.
You can solve this on your calculator, or think about it as a fraction
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Find the square of 
.
Find the square of
Squaring a decimal is identical to multiplying decimals.
Drop the decimal, multiply the number by its self, and then add up the decimal points in the original problem and put it back into your answer.
(note: 4 decimal places)
Squaring a decimal is identical to multiplying decimals.
Drop the decimal, multiply the number by its self, and then add up the decimal points in the original problem and put it back into your answer.
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If 
and 
, what is 
equal to?
If
First, we must figure out what 
is equal to.
We do 
.
Now to find out what 
is equal to, we look at 
.
We move our decimal points over so that we are dealing with only whole numbers. This gives us 
.
Finally, we count how many spaces we moved our decimals in total, and we move the decimal in our answer back that many spaces. To get from 
to 
we moved our decimal two spaces to the right. Because we did this for each of the 
values, our total spaces we moved the decimal was 
to the right.
Therefore, we must take 
and move the decimal 
places to the left. This gives us 
.
First, we must figure out what
We do
Now to find out what
We move our decimal points over so that we are dealing with only whole numbers. This gives us
Finally, we count how many spaces we moved our decimals in total, and we move the decimal in our answer back that many spaces. To get from
Therefore, we must take
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Evaluate the following:
Evaluate the following:
To solve, simply multiply 0.02 by 0.02 as though the numbers are without decimals.
Then, sum the number of spaces to the right of the decimal points in your problem and include that many in your answer.
Thus, your answer is .0004.
To solve, simply multiply 0.02 by 0.02 as though the numbers are without decimals.
Then, sum the number of spaces to the right of the decimal points in your problem and include that many in your answer.
Thus, your answer is .0004.
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If 
, 
can equal which of the following?
If
Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively. Therefore, the only answer which is within the desired range is 2/5.
Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively. Therefore, the only answer which is within the desired range is 2/5.
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Find the sum of the following:
Find the sum of the following:
To get the decimal from a fraction, divide the numerator by the denominator
To get the decimal from a fraction, divide the numerator by the denominator
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When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?
When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?
When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).
When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).
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Find the sum to the nearest hundredth:
Find the sum to the nearest hundredth:
1. Convert the fractions to decimals by division:
2. Add the corresponding whole numbers to the decimals:
3. Add the two decimals:
1. Convert the fractions to decimals by division:
2. Add the corresponding whole numbers to the decimals:
3. Add the two decimals:
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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?
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?
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.
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.
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An acid-water solution is made in which 65% of the solution is water by volume. How many liters of acid are there in 50 liters of the solution?
An acid-water solution is made in which 65% of the solution is water by volume. How many liters of acid are there in 50 liters of the solution?
35% of the solution is acid, therefore 0.35 * 50 = 17.5.
35% of the solution is acid, therefore 0.35 * 50 = 17.5.
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0.3 < 1/3
4 > √17
1/2 < 1/8
–|–6| = 6
Which of the above statements is true?
0.3 < 1/3
4 > √17
1/2 < 1/8
–|–6| = 6
Which of the above statements is true?
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.
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.
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Which of the following numbers is between 1/5 and 1/6?
Which of the following numbers is between 1/5 and 1/6?
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.
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.
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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?
The ogre under the bridge eats
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%
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%
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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.
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.
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How much less is 
than 
?
How much less is
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Write the following fraction as a decimal rounded to three decimal places: 
Write the following fraction as a decimal rounded to three decimal places:
This is a problem best solved with a calculator, but we will also cover how to work it out by hand, as well as how to eliminate a few answers.
The given fraction is very close to 
, which means it should just be a little below 
. Eliminate any answers which are greater than 
. You can solve this problem more precisely by using your calculator; by dividing 
by 
, you end up with the answer 
. Rounding to three decimal places means rounding that answer up to 
, the correct answer.
To work this out by hand, set the problem up as division problem with 
underneath the division sign:
This is a problem best solved with a calculator, but we will also cover how to work it out by hand, as well as how to eliminate a few answers.
The given fraction is very close to
To work this out by hand, set the problem up as division problem with
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If , can equal which of the following?
If
Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively. Therefore, the only answer which is within the desired range is 2/5.
Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively. Therefore, the only answer which is within the desired range is 2/5.
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Find the sum of the following:
Find the sum of the following:
To get the decimal from a fraction, divide the numerator by the denominator
To get the decimal from a fraction, divide the numerator by the denominator
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When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?
When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?
When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).
When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).
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Find the sum to the nearest hundredth:
Find the sum to the nearest hundredth:
1. Convert the fractions to decimals by division:
2. Add the corresponding whole numbers to the decimals:
3. Add the two decimals:
1. Convert the fractions to decimals by division:
2. Add the corresponding whole numbers to the decimals:
3. Add the two decimals:
Compare your answer with the correct one above