Decimal & Fraction Tests — Pick a Level and Start
Tap a level to see every test in it. Start at Level 1 the day you finish the conversion rules, then move to Level 2 with the timer running to push accuracy under pressure.
Level 1 Basic Checking… View tests
One rule applied cleanly — is the decimal terminating or recurring, turn 0.45 into a fraction, pick the largest of four fractions, evaluate a three-layer continued fraction, and the 99-type product. Attempt these without the clock while the rules are still fresh.
Level 2 Tier I Standard Checking… View tests
Real SSC CGL Tier I difficulty — two ideas chained in one question: a continued fraction with a recurring decimal inside it, a comparison that first needs a conversion, the digit at the 2026th decimal place, and fraction word problems whose answer must then be classified. This is the score that tells you the chapter is exam-ready.
Decimal and fraction is one of the steadiest scorers in the SSC CGL Quantitative Aptitude paper. A shift almost always carries one question that belongs to it outright — a recurring decimal to be written as a fraction, a continued fraction to be evaluated, or a fraction that changes when something is added to its numerator and denominator — and the same skills decide how fast you get through simplification, comparison and the arithmetic word problems.
These practice tests put twenty-five decimal and fraction questions in front of you in one sitting, which is what turns the conversion rules from something you can recite into something you apply without thinking. Every question comes with a full solution and the shortcut, in English or Hindi.
How Many Decimal and Fraction Questions Are Asked in SSC CGL?
The chapter usually gets one to two direct questions, and its methods are reused inside simplification and the comparison-type questions that appear across the arithmetic block.
| Chapter | Tier I (out of 25) | Tier II Paper I (out of 30) |
|---|---|---|
| Decimal & Fraction | 1–2 | 1–2 |
| Simplification | 1–2 | 2–3 |
| Number System | 2–3 | 3–4 |
| LCM & HCF | 1–2 | 1–2 |
| Square & Cube Roots | 1 | 1–2 |
Typical spread across recent SSC CGL shifts. SSC does not publish a chapter-wise breakup, so treat these as planning ranges. Tier I maths is always 25 questions in a locked 15-minute section.
What You Will Practice in the Decimal & Fraction Chapter
Core topics
- Terminating, pure recurring and mixed recurring decimals — and telling them apart from the denominator
- Length of the repeating block, and the digit at a given decimal place
- Converting pure and mixed recurring decimals to fractions, and back
- Sums, differences, products and square roots of recurring decimals
- Comparing and ordering fractions — cross-multiplication, same-numerator and gap-from-1 tricks
- A fraction with a given denominator lying between two fractions, and counting how many there are
- Continued fractions — evaluating them, solving for an unknown inside or outside, and writing a fraction as a continued fraction
- 99, 999 and 9999-type products with a small correction fraction
- Fraction word problems — a fraction that changes when numbers are added to its parts, two fractions from their sum and product, three linked fractions, and multiply-instead-of-divide errors
Conversion rules you must know cold
| Decimal | Fraction | Example |
|---|---|---|
| 0.a | a / 9 | 0.7 = 7/9 |
| 0.ab | ab / 99 | 0.45 = 45/99 = 5/11 |
| 0.abc | abc / 999 | 0.135 = 135/999 = 5/37 |
| 0.ab | (ab − a) / 90 | 0.46 = (46 − 4)/90 = 7/15 |
| 0.abc | (abc − a) / 990 | 0.327 = (327 − 3)/990 = 18/55 |
| 0.abc | (abc − ab) / 900 | 0.123 = (123 − 12)/900 = 37/300 |
| 0.9 | 1 | exactly 1, not slightly less |
One 9 for every repeating digit, then one 0 for every non-repeating digit. Reduce the fraction at the end — 999 = 27 × 37, so three-digit blocks often reduce to 27ths or 37ths.
Terminating or recurring — read the denominator
| Lowest-terms denominator has | Decimal is | Example |
|---|---|---|
| Only 2s and 5s | Terminating | 7/40 = 0.175 |
| No 2 and no 5 | Pure recurring | 4/11 = 0.36 |
| Some 2 or 5 and another prime | Mixed recurring | 7/30 = 0.23 |
Reduce first: 9/45 looks like it should recur, but it is 1/5 = 0.2. The number of decimal places of a terminating decimal is the larger of the powers of 2 and 5 in the denominator — 7/320 has 320 = 26 × 5, so six places.
Comparing fractions — four fast tests
| Situation | Test | Example |
|---|---|---|
| Any two fractions | Cross-multiply: a/b > c/d when ad > bc | 9/13 vs 11/16 → 144 > 143, so 9/13 is larger |
| Same numerator | Larger denominator = smaller fraction | 7/15 < 7/12 < 7/11 < 7/9 |
| All close to 1 | Smaller gap from 1 = larger fraction | 23/24 > 19/20 > 15/16 > 11/12 |
| Numerator and denominator both rise by the same amounts | Fractions move steadily towards the ratio of the increases | 2/3, 3/5, 4/7, 5/9 decrease towards 1/2 |
Continued fractions
- Evaluating: start at the innermost layer, and at each layer add the whole number to the reciprocal of the value below it.
- Unknown inside: peel from the outside in — flip both sides, subtract the layer's whole number, flip again.
- Fraction to continued fraction: flip, split off the whole part, flip the remainder, repeat. 7/24 → 24/7 = 3 + 3/7 → 7/3 = 2 + 1/3, so 7/24 = 1/(3 + 1/(2 + 1/3)).
- All-ones ladder: 1 + 1/(1 + 1/(1 + …)) gives the fractions 3/2, 5/3, 8/5, 13/8 — each numerator is the sum of the previous two.
Also worth memorising
- 99 k−1⁄k × m = 100m − m/k. So 99 5/6 × 36 = 3600 − 6 = 3594, and 999 7/8 × 16 + 2 = 16000
- Least fraction to add to a sum of mixed numbers = 1 − its fractional part; least fraction to subtract = the fractional part itself
- Adding the same number to both parts of a proper fraction makes it larger; of an improper fraction, smaller
- Multiplied by p/q instead of dividing: the error is the number × (q/p − p/q)
- Two fractions from sum S and product P: (x − y)² = S² − 4P
- 0.125 = 1/8, 0.375 = 3/8, 0.625 = 5/8, 0.875 = 7/8, 0.0625 = 1/16 — convert on sight
Solved Examples — SSC CGL Decimal & Fraction
How the Decimal & Fraction Chapter Tests Work
- 25 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
- Optional 30-minute timer — with the clock to build exam speed, without it while you are still learning the rules.
- Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
- Solutions, shortcut tricks and concept notes open after you submit, question by question.
- English and हिंदी, chosen at the start of every test.
- Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.
How to Prepare Decimal & Fraction for SSC CGL
- Learn the conversion table first and test it on random decimals. 9s for repeating digits, 0s for non-repeating digits — once this is automatic, half the chapter is done.
- Always reduce before you classify. Whether a fraction terminates depends on the lowest-terms denominator; 9/45 is 1/5.
- Treat continued fractions as one method. Inside-out to evaluate, outside-in to solve for an unknown — there is nothing else to learn.
- Never compare recurring decimals by their digits. Convert to fractions and cross-multiply, or expand both to the same number of places; 0.54 and 0.54 differ from the third digit.
- Do Level 1 untimed, the same day you finish the rules. The aim is correct recall, not speed.
- Move to Level 2 with the 30-minute clock on. A conversion that takes more than twenty seconds means you are still deriving the rule instead of applying it.
- Study it with simplification. Do number system and divisibility before, and simplification right after — the four chapters share their tricks.
- Verify against a real paper. Once Level 2 is consistent, attempt a previous year paper and then a full mock test under locked sectional timing.
SSC CGL दशमलव और भिन्न (Decimal & Fraction) चैप्टर टेस्ट — हिंदी में
दशमलव और भिन्न SSC CGL गणित का एक स्थिर अंक देने वाला अध्याय है। लगभग हर शिफ्ट में इसका 1–2 प्रश्न सीधे आता है — जैसे आवर्ती दशमलव को भिन्न में बदलना, निरंतर भिन्न (continued fraction) का मान निकालना, या वह भिन्न ज्ञात करना जो अंश-हर में कुछ जोड़ने पर बदल जाती है — और यही विधियाँ सरलीकरण और तुलना वाले प्रश्नों में भी काम आती हैं।
TrickySSC पर इस अध्याय के सभी टेस्ट हिंदी में उपलब्ध हैं — प्रश्न, विकल्प, विस्तृत हल और शॉर्टकट ट्रिक सब हिंदी में। दो स्तर हैं: लेवल 1 (आधारभूत) और लेवल 2 (टियर I स्तर)। प्रत्येक टेस्ट में 25 प्रश्न, वैकल्पिक 30 मिनट का टाइमर और +2 / −0.5 की वही मार्किंग जो असली परीक्षा में होती है।
याद रखने योग्य नियम: शुद्ध आवर्ती दशमलव में दोहराने वाले समूह को उतने ही 9 के ऊपर लिखें — 0.45 = 45/99 = 5/11; मिश्र आवर्ती में सभी अंकों में से न दोहराने वाले अंक घटाकर 9 और 0 के ऊपर लिखें — 0.46 = (46 − 4)/90 = 7/15। और भिन्न तभी सांत होती है जब न्यूनतम रूप के हर में 2 और 5 के अलावा कोई अभाज्य न हो।