Decimal fractions is a chapter where nobody fails because of the concept. They fail because of the decimal point. One place counted wrong and the answer is ten times off, and the paper will have that wrong answer sitting there as an option, waiting for you. So build one habit right now, count the decimal places before you calculate, not after.
In multiplication you add the places, in division you shift them, and in addition you line them up. That is the whole chapter in one line. The other habit worth building is clearing the decimal first. Turn 0.06 divided by 0.0003 into 600 divided by 3 and the fear disappears. Learn the recurring decimal rule properly because two or three questions come from it in every paper and most students leave them.
Decimal Fractions Formulas
Decimal to fraction
Write the digits without the point on top, and 1 followed by as many zeros as there are decimal places at the bottom, then reduce.
0.25 = 25/100 = 1/4, and 0.125 = 125/1000 = 1/8
Fraction to decimal
Divide the top by the bottom.
It terminates only if the denominator, after reducing, has no prime factor other than 2 and 5. Otherwise it recurs.
Multiplying
Ignore the points, multiply as whole numbers, then count the total decimal places in both numbers and put that many in the answer.
0.2 × 0.03 = 6 with three places, so 0.006
Dividing
Shift the point in the divisor to make it a whole number, and shift the point in the dividend by the same number of places.
0.06 ÷ 0.0003, shift four places in both, so 600 ÷ 3 = 200
Dividing by 0.1 is multiplying by 10. Dividing by 0.5 is multiplying by 2.
Adding and subtracting
Line up the points one below the other, fill the short ones with zeros, then bring the point straight down.
Pure recurring decimal
Repeating digits on top, as many 9s below as there are repeating digits.
0.333… = 3/9 = 1/3, and 0.363636… = 36/99 = 4/11
Mixed recurring decimal
On top, all the digits after the point once, minus the digits that do not repeat.
Below, as many 9s as repeating digits, followed by as many 0s as non-repeating digits.
0.1666… = (16 − 1) ÷ 90 = 15/90 = 1/6
Comparing
Make the decimal places equal by adding zeros at the end, then compare like whole numbers. 0.5 is bigger than 0.409, never compare by length.
For fractions, cross multiply. For a/b and c/d, compare a × d with b × c.
Roots and powers
A square root halves the decimal places, so √0.0009 = 0.03
A cube root divides them by three, so ³√0.008 = 0.2
A square doubles them, so 0.03² = 0.0009
The identities that save time
a² − b² = (a + b) (a − b), so 0.98² − 0.02² = 1.00 × 0.96 = 0.96
(a − b)² = a² − 2ab + b², so 0.99² = 1 − 0.02 + 0.0001 = 0.9801
60 Decimal Fractions Aptitude Questions and Answers (Solved MCQs)
Question 1. What is the place value of 7 in the decimal number 43.0785?
a) 0.7
b) 0.07
c) 0.007
d) 0.0007
Answer:
b) 0.07 — The first digit after the decimal point is in the tenths place, and the second digit is in the hundredths place. Therefore, 7 is in the hundredths place and has a value of 7/100 = 0.07.
Question 2. What is the decimal equivalent of 7/32?
a) 0.20875
b) 0.21875
c) 0.22875
d) 0.28125
Answer:
b) 0.21875 — Dividing 7 by 32 gives 0.21875. Alternatively, multiplying the numerator and denominator by 3,125 gives 21,875/100,000 = 0.21875.
Question 3. What is the simplest fractional form of 0.0375?
a) 3/40
b) 3/80
c) 5/80
d) 15/200
Answer:
b) 3/80 — We have 0.0375 = 375/10,000. Dividing the numerator and denominator by 125 gives 3/80.
Question 4. Which of the following fractions has a terminating decimal expansion?
a) 5/21
b) 7/40
c) 11/42
d) 13/45
Answer:
b) 7/40 — A fraction in its simplest form has a terminating decimal expansion only when its denominator contains no prime factors other than 2 and 5. Since 40 = 2³×5, the fraction 7/40 terminates.
Question 5. What is the value of 18.75+6.084−9.936?
a) 14.798
b) 14.898
c) 14.998
d) 15.898
Answer:
b) 14.898 — First, 18.75+6.084 = 24.834. Subtracting 9.936 gives 24.834−9.936 = 14.898.
Question 6. What is the value of 4.8×0.075?
a) 0.036
b) 0.36
c) 3.6
d) 36
Answer:
b) 0.36 — Ignoring the decimal points initially, 48×75 = 3,600. The factors contain a total of four decimal places, so the product is 0.3600 = 0.36.
Question 7. What is the value of 12.096÷0.24?
a) 5.04
b) 50.4
c) 504
d) 0.504
Answer:
b) 50.4 — Multiplying both the dividend and divisor by 100 gives 1,209.6÷24. Since 24×50.4 = 1,209.6, the required value is 50.4.
Question 8. Which of the following is the smallest decimal number?
a) 0.505
b) 0.550
c) 0.055
d) 0.5005
Answer:
c) 0.055 — Writing the decimals with equal numbers of places gives 0.5050, 0.5500, 0.0550 and 0.5005. Clearly, 0.0550 is the smallest.
Question 9. What is the value of 0.00072×105?
a) 0.72
b) 7.2
c) 72
d) 720
Answer:
c) 72 — Multiplication by 10⁵ moves the decimal point five places to the right. Therefore, 0.00072×100,000 = 72.
Question 10. What is the value of (2.4)²−(1.6)²?
a) 2.8
b) 3.2
c) 3.6
d) 4.0
Answer:
b) 3.2 — Using a²−b² = (a−b)(a+b), we get (2.4−1.6)(2.4+1.6) = 0.8×4 = 3.2.
Question 11. What is the value of (0.125×0.08)÷0.005?
a) 0.2
b) 0.5
c) 2
d) 5
Answer:
c) 2 — First, 0.125×0.08 = 0.01. Therefore, 0.01÷0.005 = 2.
Question 12. If 3.75x = 0.9375, what is the value of x?
a) 0.20
b) 0.25
c) 0.30
d) 0.40
Answer:
b) 0.25 — Dividing both sides by 3.75 gives x = 0.9375/3.75. Since 3.75×0.25 = 0.9375, x = 0.25.
Question 13. Which statement correctly compares 0.7, 0.70 and 0.700?
a) 0.7 < 0.70 < 0.700
b) 0.7 > 0.70 > 0.700
c) 0.7 = 0.70 = 0.700
d) 0.7 = 0.70 < 0.700
Answer:
c) 0.7 = 0.70 = 0.700 — Adding zeros to the right of the final digit in a decimal number does not change its value. Therefore, all three decimals are equal.
Question 14. What is the value of 5.04÷(0.7×1.2)?
a) 5
b) 6
c) 7
d) 8
Answer:
b) 6 — First, 0.7×1.2 = 0.84. Therefore, 5.04÷0.84 = 6.
Question 15. What is the value of [(0.2)−2+(0.5)−2]−1?
a) 1/21
b) 1/25
c) 1/29
d) 1/31
Answer:
c) 1/29 — We have (0.2)−2 = (1/5)−2 = 25 and (0.5)−2 = (1/2)−2 = 4. Their sum is 29. Therefore, 29−1 = 1/29.
Question 16. What is the fractional form of 0.7777…?
a) 7/10
b) 7/9
c) 8/9
d) 9/7
Answer:
b) 7/9 — Let x = 0.7777…. Then 10x = 7.7777…. Subtracting x from 10x gives 9x = 7. Therefore, x = 7/9.
Question 17. What is the simplest fractional form of 0.272727…?
a) 2/11
b) 3/11
c) 27/100
d) 27/90
Answer:
b) 3/11 — Let x = 0.272727…. Since two digits repeat, 100x = 27.272727…. Subtracting gives 99x = 27. Therefore, x = 27/99 = 3/11.
Question 18. What is the simplest fractional form of 0.16666…, where only 6 repeats?
a) 1/5
b) 1/6
c) 1/8
d) 1/9
Answer:
b) 1/6 — Let x = 0.16666…. Then 10x = 1.6666… and 100x = 16.6666…. Subtracting gives 90x = 15. Therefore, x = 15/90 = 1/6.
Question 19. What is the simplest fractional form of 2.454545…?
a) 25/11
b) 27/11
c) 49/20
d) 245/99
Answer:
b) 27/11 — Let x = 2.454545…. Then 100x = 245.454545…. Subtracting x gives 99x = 243. Therefore, x = 243/99 = 27/11.
Question 20. What is the simplest fractional form of 0.123123123…?
a) 41/333
b) 41/300
c) 123/900
d) 123/990
Answer:
a) 41/333 — Let x = 0.123123123…. Since three digits repeat, 1,000x = 123.123123…. Subtracting gives 999x = 123. Therefore, x = 123/999 = 41/333.
Question 21. What is the simplest fractional form of 0.083333…, where only 3 repeats?
a) 1/10
b) 1/11
c) 1/12
d) 1/15
Answer:
c) 1/12 — Let x = 0.083333…. Then 100x = 8.3333… and 1,000x = 83.3333…. Subtracting gives 900x = 75. Therefore, x = 75/900 = 1/12.
Question 22. What is the value of 0.8888…−0.2222…?
a) 1/3
b) 1/2
c) 2/3
d) 7/9
Answer:
c) 2/3 — We have 0.8888… = 8/9 and 0.2222… = 2/9. Therefore, their difference is 8/9−2/9 = 6/9 = 2/3.
Question 23. What is the value of 0.3333…+0.6666…?
a) 0.9
b) 0.99
c) 0.999
d) 1
Answer:
d) 1 — We have 0.3333… = 1/3 and 0.6666… = 2/3. Therefore, their sum is 1/3+2/3 = 1.
Question 24. In its simplest form, a fraction has the denominator 2⁴×5³. After how many decimal places will its decimal expansion terminate?
a) 3
b) 4
c) 5
d) 7
Answer:
b) 4 — To express the denominator as a power of 10, the powers of 2 and 5 must be equal. Multiplying by 5 gives 2⁴×5⁴ = 10⁴. Therefore, the decimal expansion terminates after at most four decimal places.
Question 25. What is the decimal equivalent of 7/125?
a) 0.0056
b) 0.056
c) 0.56
d) 5.6
Answer:
b) 0.056 — Multiplying the numerator and denominator by 8 gives 56/1,000. Therefore, 7/125 = 0.056.
Question 26. What is 18.4765 rounded to three decimal places?
a) 18.476
b) 18.477
c) 18.480
d) 18.487
Answer:
b) 18.477 — The third decimal digit is 6, and the next digit is 5. Therefore, the third decimal digit is increased by 1, giving 18.477.
Question 27. What is 0.004786 rounded to three significant figures?
a) 0.00478
b) 0.00479
c) 0.00480
d) 0.00500
Answer:
b) 0.00479 — The first three significant digits are 4, 7 and 8. The next digit is 6, so 8 is rounded up to 9. Therefore, the number rounded to three significant figures is 0.00479.
Question 28. Which of the following is exactly equal to 0.9999…?
a) 0.9
b) 0.99
c) 0.999
d) 1
Answer:
d) 1 — Let x = 0.9999…. Then 10x = 9.9999…. Subtracting gives 9x = 9, so x = 1. Therefore, 0.9999… is exactly equal to 1.
Question 29. How many digits are there in the smallest repeating block of the decimal expansion of 1/7?
a) 3
b) 4
c) 5
d) 6
Answer:
d) 6 — The decimal expansion of 1/7 is 0.142857142857…. The repeating block is 142857, which contains six digits.
Question 30. What is the simplest fractional form of 0.123333…, where only 3 repeats?
a) 17/150
b) 37/300
c) 41/333
d) 123/1,000
Answer:
b) 37/300 — Write the number as 0.12+0.003333…. Now, 0.12 = 36/300, and 0.003333… = 1/300. Therefore, the number is 36/300+1/300 = 37/300.
Question 31. A customer purchases 2.75 kg of rice at ₹48.60 per kg. What is the total cost?
a) ₹131.65
b) ₹132.75
c) ₹133.65
d) ₹134.75
Answer:
c) ₹133.65 — The total cost is 2.75×48.60. This equals 48.60×(2+0.75) = 97.20+36.45 = ₹133.65.
Question 32. A piece of cloth is 12.5 metres long. If 3.75 metres and 2.8 metres are cut from it, how much cloth remains?
a) 5.85 metres
b) 5.95 metres
c) 6.05 metres
d) 6.15 metres
Answer:
b) 5.95 metres — The total length removed is 3.75+2.80 = 6.55 metres. Therefore, the remaining length is 12.50−6.55 = 5.95 metres.
Question 33. A car covers 184.8 km in 3.5 hours. What is its average speed?
a) 50.8 km/h
b) 51.6 km/h
c) 52.8 km/h
d) 54.2 km/h
Answer:
c) 52.8 km/h — Average speed = distance/time = 184.8/3.5. Multiplying both numbers by 10 gives 1,848/35 = 52.8 km/h.
Question 34. What is the average of 12.4, 15.75, 9.85 and 14?
a) 12.5
b) 13
c) 13.25
d) 14
Answer:
b) 13 — The sum is 12.4+15.75+9.85+14 = 52. Therefore, the average is 52/4 = 13.
Question 35. An article marked at ₹1,250 is sold at a discount of 12.5%. What is its selling price?
a) ₹1,078.25
b) ₹1,093.75
c) ₹1,100.50
d) ₹1,125.00
Answer:
b) ₹1,093.75 — The discount is 12.5% of ₹1,250 = 0.125×1,250 = ₹156.25. Therefore, the selling price is ₹1,250−₹156.25 = ₹1,093.75.
Question 36. An item is purchased for ₹480 and sold for ₹552. What is the profit percentage?
a) 12.5%
b) 15%
c) 17.5%
d) 20%
Answer:
b) 15% — The profit is ₹552−₹480 = ₹72. Therefore, the profit percentage is 72/480×100 = 15%.
Question 37. What is 3.475 kilometres expressed in metres?
a) 347.5 metres
b) 3,047.5 metres
c) 3,475 metres
d) 34,750 metres
Answer:
c) 3,475 metres — One kilometre equals 1,000 metres. Therefore, 3.475 kilometres = 3.475×1,000 = 3,475 metres.
Question 38. A tank contains 125.5 litres of water. After 38.75 litres are drained and 12.6 litres are added, how much water does the tank contain?
a) 97.35 litres
b) 98.25 litres
c) 99.35 litres
d) 100.45 litres
Answer:
c) 99.35 litres — After draining, the tank contains 125.50−38.75 = 86.75 litres. Adding 12.60 litres gives 86.75+12.60 = 99.35 litres.
Question 39. Eighteen identical machines manufacture 24.75 units each during a shift. How many units do they manufacture altogether?
a) 425.5
b) 435.5
c) 445.5
d) 455.5
Answer:
c) 445.5 — The total production is 18×24.75. This equals 24.75×(20−2) = 495−49.5 = 445.5 units.
Question 40. A length is measured as 25.2 cm, while its actual value is 24.8 cm. What is the percentage error, correct to two decimal places?
a) 1.21%
b) 1.41%
c) 1.61%
d) 1.81%
Answer:
c) 1.61% — The absolute error is 25.2−24.8 = 0.4 cm. Percentage error = 0.4/24.8×100 ≈ 1.6129%. Correct to two decimal places, this is 1.61%.
Question 41. How is 0.0000845 written in scientific notation?
a) 8.45×10−4
b) 8.45×10−5
c) 84.5×10−5
d) 0.845×10−6
Answer:
b) 8.45×10−5 — Moving the decimal point five places to the right produces 8.45. Therefore, 0.0000845 = 8.45×10−5.
Question 42. What is the simplest form of the ratio 1.2:0.45?
a) 4:3
b) 8:3
c) 8:5
d) 12:5
Answer:
b) 8:3 — Multiplying both terms by 100 gives 120:45. Dividing both terms by 15 gives 8:3.
Question 43. What is the simple interest on ₹2,400 at 7.5% per annum for 2 years?
a) ₹320
b) ₹340
c) ₹360
d) ₹380
Answer:
c) ₹360 — Simple interest = Principal×Rate×Time/100. Therefore, the interest is 2,400×7.5×2/100 = ₹360.
Question 44. A vehicle travels 18.75 km per litre of fuel. How many litres are required to travel 240 km?
a) 11.8 litres
b) 12.5 litres
c) 12.8 litres
d) 13.2 litres
Answer:
c) 12.8 litres — Fuel required = distance/mileage = 240/18.75. Multiplying both numbers by 100 gives 24,000/1,875 = 12.8 litres.
Question 45. A shopkeeper mixes 12.5 kg of rice costing ₹64.80 per kg with 7.5 kg of rice costing ₹72.80 per kg. What is the average cost per kilogram of the mixture?
a) ₹66.80
b) ₹67.20
c) ₹67.80
d) ₹68.40
Answer:
c) ₹67.80 — The cost of the first variety is 12.5×64.80 = ₹810. The cost of the second variety is 7.5×72.80 = ₹546. The total cost is ₹1,356 for 20 kg. Therefore, the average cost is 1,356/20 = ₹67.80 per kg.
Question 46. What is the value of (0.0048×0.075)÷0.00012?
a) 0.3
b) 3
c) 30
d) 300
Answer:
b) 3 — First, 0.0048×0.075 = 0.00036. Therefore, 0.00036÷0.00012 = 3.
Question 47. If x = 0.16666… and y = 0.08333…, what is the value of x/y?
a) 1/2
b) 1
c) 2
d) 4
Answer:
c) 2 — We have x = 1/6 and y = 1/12. Therefore, x/y = (1/6)÷(1/12) = (1/6)×12 = 2.
Question 48. What is the value of 0.272727…÷0.090909…?
a) 2
b) 3
c) 4
d) 6
Answer:
b) 3 — We have 0.272727… = 27/99 = 3/11 and 0.090909… = 9/99 = 1/11. Therefore, the quotient is (3/11)÷(1/11) = 3.
Question 49. What is the value of 0.000729÷0.09?
a) 0.00081
b) 0.0081
c) 0.081
d) 0.81
Answer:
b) 0.0081 — Multiplying the dividend and divisor by 100 gives 0.0729÷9. Since 0.0729/9 = 0.0081, the required value is 0.0081.
Question 50. A quantity is first increased by 25% and then decreased by 20%. What is the overall percentage change?
a) 5% increase
b) 5% decrease
c) No change
d) 10% decrease
Answer:
c) No change — The successive multiplication factors are 1.25 and 0.80. Their product is 1.25×0.80 = 1. Therefore, the final quantity equals the original quantity.
Question 51. Using each of the digits 0, 2, 4 and 7 exactly once after the decimal point, what is the smallest decimal number greater than 0.2?
a) 0.2047
b) 0.2074
c) 0.2407
d) 0.2470
Answer:
a) 0.2047 — To obtain the smallest number greater than 0.2, the tenths digit must be 2. The remaining digits 0, 4 and 7 must then be arranged in increasing order. Therefore, the smallest possible number is 0.2047.
Question 52. What is the product of the integer part and the fractional part of 17.625?
a) 9.625
b) 10.125
c) 10.625
d) 11.625
Answer:
c) 10.625 — The integer part is 17, and the fractional part is 0.625. Their product is 17×0.625 = 10.625.
Question 53. What is the value of [(0.384)²−(0.216)²]÷0.168?
a) 0.5
b) 0.6
c) 0.8
d) 1.0
Answer:
b) 0.6 — Using a²−b² = (a−b)(a+b), the numerator becomes (0.384−0.216)(0.384+0.216) = 0.168×0.600. Dividing by 0.168 gives 0.600.
Question 54. If 0.2x+0.03 = 0.15x+0.28, what is the value of x?
a) 4
b) 5
c) 6
d) 7
Answer:
b) 5 — Rearranging gives 0.2x−0.15x = 0.28−0.03. Therefore, 0.05x = 0.25, so x = 5.
Question 55. What is the value of (0.01)−1/2?
a) 0.1
b) 1
c) 10
d) 100
Answer:
c) 10 — Since 0.01 = 1/100, its square root is 0.1. Therefore, (0.01)−1/2 is the reciprocal of 0.1, which is 10.
Question 56. What is the value of 1/0.2+1/0.25−1/0.5?
a) 5
b) 6
c) 7
d) 9
Answer:
c) 7 — We have 1/0.2 = 5, 1/0.25 = 4 and 1/0.5 = 2. Therefore, the required value is 5+4−2 = 7.
Question 57. What is the next term in the decimal sequence 0.2, 0.06, 0.018, 0.0054, …?
a) 0.000162
b) 0.00108
c) 0.00162
d) 0.0162
Answer:
c) 0.00162 — Each term is obtained by multiplying the preceding term by 0.3. Therefore, the next term is 0.0054×0.3 = 0.00162.
Question 58. A number multiplied by 0.125 gives 7.5. What is the number?
a) 48
b) 56
c) 60
d) 64
Answer:
c) 60 — Let the number be x. Then 0.125x = 7.5. Since 0.125 = 1/8, we have x/8 = 7.5. Therefore, x = 7.5×8 = 60.
Question 59. What is the exact value of 49.98×2.004?
a) 99.95992
b) 100.05992
c) 100.15992
d) 100.19992
Answer:
c) 100.15992 — Write 2.004 as 2+0.004. Then 49.98×2 = 99.96 and 49.98×0.004 = 0.19992. Therefore, the exact product is 99.96+0.19992 = 100.15992.
Question 60. What is the simplest fractional form of 0.123333…−0.076666…, where only the final displayed digit repeats in each decimal?
a) 7/150
b) 7/100
c) 14/225
d) 23/300
Answer:
a) 7/150 — We have 0.123333… = 37/300. Also, 0.076666… = 0.07+0.006666… = 21/300+2/300 = 23/300. Therefore, the difference is 37/300−23/300 = 14/300 = 7/150.
