How to find the decimal equivalent of a fraction
Help Questions
ACT Math › How to find the decimal equivalent of a fraction
Find the sum of the following:
Explanation
To get the decimal from a fraction, divide the numerator by the denominator
When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?
0
1
2
4
5
Explanation
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).
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?
17.5
32.5
12.5
38.5
Explanation
35% of the solution is acid, therefore 0.35 * 50 = 17.5.
Find the sum to the nearest hundredth:
Explanation
1. Convert the fractions to decimals by division:
2. Add the corresponding whole numbers to the decimals:
3. Add the two decimals:
If 
None of the other answer choices are correct
Explanation
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.
The ogre under the bridge eats 
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%
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?
8/9
2/7
3/5
9/15
1/10
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.
Which of the following numbers is between 1/5 and 1/6?
0.25
0.22
0.19
0.16
0.13
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.
0.01
0.04
0.05
0.07
0.10
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.
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
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.