Decimals & Fractions — RRB NTPC Mathematics
This topic carries roughly 5% of Mathematics's 30 questions. It rarely appears as a standalone hard question — its real role is as the quiet first step inside a percentage, ratio, or interest problem elsewhere in the paper, where a fraction-conversion slip produces a confidently wrong final answer.
1. What RRB NTPC actually asks
Expect direct fraction arithmetic (addition, subtraction, multiplication, division of fractions with unlike denominators), decimal-to-fraction and fraction-to-decimal conversion, comparison and ordering of mixed decimal/fraction values, and simplification of expressions combining both forms.
2. Converting between decimals and fractions
A terminating decimal converts directly: count the digits after the decimal point, and that's the power of 10 in the denominator. 0.375 = 375/1000 = 3/8 after simplifying.
A recurring decimal needs the standard algorithm: let x = 0.1666..., then 10x = 1.666..., and 100x = 16.666.... Subtracting, 90x = 15, so x = 15/90 = 1/6.
3. Comparing fractions and decimals
To compare fractions with different denominators, convert to a common denominator (the LCM of the denominators) or convert every value to its decimal form and compare directly — decimal comparison is usually faster under exam time pressure since it avoids finding an LCM.
Values that look different can be equal. 3/5 and 0.6 are the same number in different forms — always check this before assuming two options are distinct.
4. Fraction arithmetic
Addition and subtraction require a common denominator; multiplication multiplies numerators and denominators directly; division multiplies by the reciprocal of the divisor. These rules don't change — the only source of error is arithmetic care, particularly in finding the correct LCM for a common denominator.
Worked examples
Q1. Convert 0.375 to its simplest fraction form.
Pick an option to check your answer.
Show explanation
Solution. 0.375 = 375/1000. The HCF of 375 and 1000 is 125. Dividing both by 125: 375÷125 = 3, 1000÷125 = 8, giving 3/8.
(a) has an incorrect denominator. (c) and (d) result from an incomplete or incorrect simplification of 375/1000. Answer: (b).
Q2. Which of the following is the greatest: 0.6, 5/9, 0.55, 7/12?
Pick an option to check your answer.
Show explanation
Solution. Converting all to decimals for direct comparison: 0.6, 5/9 ≈ 0.556, 0.55, 7/12 ≈ 0.583.
Ordering these: 0.55 < 5/9 (≈0.556) < 7/12 (≈0.583) < 0.6. The greatest value is 0.6. Answer: (a).
6. Common traps
- Assuming two differently-written values must be different numbers. Always convert to a common form (usually decimal) before comparing — 3/5 and 0.6 are identical.
- Forgetting to simplify a fraction to its lowest terms after converting from a decimal — an unsimplified fraction like 375/1000 is not wrong arithmetically, but it won't match a simplified option like 3/8.
- Using the wrong common denominator in fraction addition or subtraction — always use the LCM of the denominators, not their product, to avoid unnecessarily large numbers that increase the chance of a slip.
- Dividing by a fraction without inverting it — division by a/b means multiplying by b/a, not a/b.
7. Guessing strategy
A quick decimal-value estimate (even to one decimal place) is usually enough to eliminate at least one of four options in a comparison question, which is the threshold needed for a guess to have non-negative expected value under 1/3 negative marking.
Summary
- Decimals & Fractions is roughly 5% of Mathematics's 30 CBT 1 questions, and often shows up embedded inside other question types rather than standalone.
- Terminating decimals convert directly by counting decimal places; recurring decimals need the subtract-and-solve algorithm.
- Converting to decimal form is usually the fastest way to compare fractions with unlike denominators.
- Always check whether two differently-written values are actually equal before assuming they're distinct options.
- Fraction addition/subtraction needs a common denominator (use the LCM); division means multiplying by the reciprocal.
- A rough one-decimal-place estimate is usually enough to eliminate an option and clear the guessing threshold.
