Decimal fractions look simple, yet they sit underneath percentages, profit-loss, averages and almost every other AFCAT Numerical Ability topic. If your decimal handling is slow or careless, every other chapter suffers. This Cavalier guide rebuilds your decimal basics, then hands you the speed tricks and shortcuts that turn long sums into ten-second answers under exam pressure.
Why Decimal Fractions Are a Foundation Skill
In AFCAT Numerical Ability you rarely see a question that announces “this is a decimal fractions sum”. Instead, decimals hide everywhere — a percentage written as 0.15, a rate of speed like 12.5 km/h, a price of ₹47.50, an average of 36.8. If you cannot move decimal points quickly and safely, you bleed both time and accuracy across the whole paper.
Because AFCAT carries negative marking (1 mark lost for every wrong answer against 3 gained for a correct one), a single misplaced decimal point can flip an easy 3 marks into a minus-1. So this chapter is less about hard theory and more about disciplined, fast technique.
Think about how the paper actually flows. You have roughly two minutes per question on average, but the difficult comprehension or data-interpretation items can eat four or five minutes each. The only way to buy that time is to finish the routine arithmetic — much of it decimal work — in well under a minute. Candidates who clear the cut-off almost always share one habit: they have made decimal calculation so automatic that it no longer feels like effort. That is the standard this chapter is written to build.
Treat decimals as your warm-up topic. Master them first, and percentages, ratio, profit-loss and data interpretation all become noticeably faster.
What Exactly Is a Decimal Fraction
A decimal fraction is simply a fraction whose denominator is a power of ten — 10, 100, 1000 and so on — written in a compact form using a decimal point.
- 7/10 is written as 0.7
- 23/100 is written as 0.23
- 9/1000 is written as 0.009
The digits after the decimal point follow strict place values: the first place is tenths, the second is hundredths, the third is thousandths. So in 0.246 the 2 means 2 tenths, the 4 means 4 hundredths and the 6 means 6 thousandths.
Notice that the place value gets ten times smaller with every step to the right, just as whole-number place value gets ten times bigger with every step to the left. The decimal point is simply the boundary between the whole part and the fractional part. Understanding this single idea — that everything is built on powers of ten — explains every rule that follows. There is nothing to memorise blindly: each shortcut is just place value working for you.
It also helps to read a decimal correctly. 0.246 is read as “zero point two four six”, not “zero point two hundred forty-six”. Reading digit by digit keeps the place values straight and stops the common slip of treating the decimal part as an ordinary number.
Adding zeros at the end of the decimal part never changes the value: 0.5 = 0.50 = 0.500. This trick lets you line up decimals of different lengths for easy comparison and subtraction.
Adding and Subtracting Decimals Safely
The golden rule is one line long: line up the decimal points, one below the other, and then add or subtract exactly as you would whole numbers.
If the numbers have unequal decimal places, fill the gaps with trailing zeros so every number has the same number of decimal digits. This single habit removes almost all careless mistakes.
Find 12.6 + 4.75 + 0.084.
The same rule applies to subtraction. If you must compute 8 − 3.276, first write 8 as 8.000 so both numbers have three decimal places, then subtract column by column to get 4.724. Writing the whole number with its trailing zeros prevents the panic many candidates feel when one number “has no decimals”.
Right-aligning the digits like ordinary numbers instead of aligning the decimal points. Always align the points first — the digits will fall into place on their own.
Multiplying Decimals the Fast Way
Forget the decimal points while you multiply. Use this three-step shortcut:
- Ignore the points and multiply the numbers as whole numbers.
- Count the total decimal places in both original numbers.
- In the answer, place the decimal point so it has that many digits after it.
Find 1.2 × 0.05.
Multiplying by 10, 100, 1000 just shifts the point right by 1, 2, 3 places. Dividing by them shifts it left. This alone answers many quick questions instantly.
Dividing Decimals Without Confusion
Division scares candidates only because of the point. The fix is to turn the divisor into a whole number first.
Multiply both the divisor and the dividend by the same power of ten so the divisor becomes a whole number. The value of the answer does not change, but the sum becomes ordinary division.
Find 4.5 ÷ 0.15.
One more division idea saves time: if the dividend and divisor share a common factor, cancel it before dividing. For 4.5 ÷ 1.5 you do not need any point-shifting at all — both are multiples of 1.5, so the answer is simply 3. Trained eyes spot these shortcuts instantly and skip the formal method.
When you shift the point in the divisor, shift it the same number of places in the dividend. Equal shifts keep the answer correct.
Converting Between Decimals and Fractions
Many AFCAT questions are solved faster in fraction form, so this conversion is a core speed skill.
Decimal to fraction
Write the digits after the point over the matching power of ten, then simplify.
- 0.75 = 75/100 = 3/4
- 0.6 = 6/10 = 3/5
- 0.125 = 125/1000 = 1/8
Fraction to decimal
Divide the numerator by the denominator, or convert the denominator into a power of ten.
- 3/4 = 75/100 = 0.75
- 1/8 = 125/1000 = 0.125
Why does this matter for speed? Because some operations are far easier in one form than the other. Multiplying 0.625 × 16 looks ugly, but rewriting 0.625 as 5/8 turns it into 5/8 × 16 = 10 in a single step. The exam reward goes to the candidate who can switch fluidly between the two forms and pick whichever makes the arithmetic shortest.
Memorise the common conversions: 1/2 = 0.5, 1/4 = 0.25, 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 1/5 = 0.2, 1/3 ≈ 0.333, 2/3 ≈ 0.667. These appear in percentages and ratio questions constantly.
Terminating and Recurring Decimals
A terminating decimal ends after a finite number of digits, like 0.25 or 0.8. A recurring (repeating) decimal has a digit or block that repeats forever, like 0.333… or 0.142857142857…
Quick test: write the fraction in lowest terms. If the denominator has only 2s and 5s as prime factors, the decimal terminates. Any other prime factor (3, 7, 11…) makes it recurring.
- 7/40 → 40 = 23 × 5 → terminates (0.175)
- 5/12 → 12 = 22 × 3 → recurs (0.41666…)
To write a pure recurring decimal as a fraction, put the repeating block over an equal number of nines. So 0.4̅ = 4/9 and 0.27̅ = 27/99 = 3/11.
If a sum gives an endless decimal, switch to the fraction form early. Carrying 0.41666… through a calculation invites rounding errors and lost marks.
Comparing and Ordering Decimals Fast
Comparing decimals trips up candidates who think “more digits means larger”. That is false: 0.7 is bigger than 0.65 even though 0.65 has more digits.
The reliable method is to equalise the decimal places with trailing zeros, then compare digit by digit from the left.
Arrange in ascending order: 0.7, 0.65, 0.709, 0.71.
Assuming a longer decimal is automatically larger. Always pad with zeros so every number has equal places before you compare.
Time-Saving Decimal Shortcuts for AFCAT
These quick tricks save precious seconds in the actual paper.
- × 0.5 means halve the number. 48 × 0.5 = 24.
- × 0.25 means take one-fourth. 80 × 0.25 = 20.
- × 0.1, 0.01, 0.001 just shift the point left by 1, 2, 3 places.
- ÷ 0.5 means double the number. 36 ÷ 0.5 = 72.
- ÷ 0.25 means multiply by 4. 9 ÷ 0.25 = 36.
The logic is simple: 0.5 = 1/2, 0.25 = 1/4, 0.2 = 1/5. Replacing the decimal with its fraction turns an awkward multiplication into an instant mental step. Drilling these conversions until they are automatic is the single biggest time-saver in this chapter.
Memorise: dividing by a decimal less than 1 makes the number bigger; multiplying by a decimal less than 1 makes it smaller. This sanity check catches most careless errors.
Estimation and Sanity Checks
Under time pressure, a rough estimate often tells you the answer without exact working. Round each decimal to the nearest whole number, do the easy sum, and match it to the closest option.
For example, 19.8 × 4.97 is approximately 20 × 5 = 100, so any option far from 100 can be eliminated at a glance. Then refine only if two options sit close together.
Always run a final sanity check on the magnitude of your answer. If you multiplied two numbers each less than 1 and your answer is bigger than 1, something is wrong — the true answer must be smaller than both.
In a multiple-choice exam, you do not always need the exact value — you need the right option. Estimation plus elimination is often faster and safer than full computation.
Build estimation into your mock-test routine. Before you start the precise calculation, jot a rough answer in the margin. When your exact working lands far from that estimate, you have an early warning of a slipped decimal point and a chance to fix it before locking the answer. This two-second habit, practised over a few dozen mocks, quietly removes most of the careless errors that cost candidates their cut-off.
Previous-Year Style Question
Q. The value of (0.96 × 0.96 − 0.04 × 0.04) ÷ (0.96 − 0.04) is:
(a) 0.92 (b) 1.00 (c) 0.96 (d) 1.04
Answer: (b) 1.00. The numerator is a2 − b2 = (a + b)(a − b) with a = 0.96, b = 0.04. So it becomes (0.96 + 0.04)(0.96 − 0.04) ÷ (0.96 − 0.04) = (0.96 + 0.04) = 1.00. Spotting the a2 − b2 identity avoids all the messy decimal multiplication.
Quick Revision Recap
- A decimal fraction has a denominator that is a power of ten; place value runs tenths, hundredths, thousandths.
- To add or subtract, line up the decimal points and pad with trailing zeros.
- To multiply, ignore the points, multiply, then count total decimal places for the answer.
- To divide, make the divisor a whole number and shift the dividend equally.
- Learn key conversions: 0.5 = 1/2, 0.25 = 1/4, 0.125 = 1/8, 0.2 = 1/5.
- Compare by padding to equal places; use estimation and a magnitude sanity check to avoid traps.
Frequently asked questions
How important are decimal fractions for AFCAT?
Very important as a foundation. Decimals appear directly in a few questions and indirectly inside percentages, ratio, speed, averages and profit-loss, so fast decimal handling speeds up the entire Numerical Ability section.
What is the quickest way to multiply two decimals?
Ignore the decimal points and multiply the numbers as whole numbers, then count the total number of decimal places in both original numbers and place the point so the answer has that many decimal digits.
How do I divide by a decimal number?
Multiply both the divisor and the dividend by the same power of ten so the divisor becomes a whole number, then divide normally. Equal shifts keep the answer value unchanged.
How can I tell if a fraction gives a terminating decimal?
Write the fraction in lowest terms. If the denominator has only 2 and 5 as prime factors the decimal terminates; any other prime factor such as 3, 7 or 11 makes it a recurring decimal.
Is a decimal with more digits always larger?
No. Compare by padding all numbers with trailing zeros to equal decimal places, then compare digit by digit from the left. For example 0.7 is larger than 0.65 even though it has fewer digits.
Related AFCAT Numerical Ability topics
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