1. What is Estimation?
Estimation means obtaining a value that is sufficiently close to the exact answer without performing every calculation exactly. In competitive examinations, estimation is especially useful when the question asks for a nearest or approximate value, or when the answer options are far apart.
Key Idea:
The objective of estimation is not to obtain a random rough answer. It is to obtain a value that is accurate enough to identify the correct option quickly.
Example:
49.7 × 20.1
49.7 ≈ 50
20.1 ≈ 20
Estimated product ≈ 50×20 = 1000.
Exam Tip:
Estimation is most powerful when exact calculation is lengthy but the options are widely separated.
2. Rounding, Estimation and Nearest-Value Method
These three ideas are related but not identical.
| Method | Meaning | Main Use |
|---|
| Rounding | Replacing a number according to a fixed place-value rule | Nearest integer, ten, decimal place, etc. |
| Estimation | Replacing values by convenient nearby values | Fast calculation |
| Nearest-Value Method | Estimating sufficiently accurately to identify the closest option | Multiple-choice exams |
Observation:
Nearest-value questions do not always require every number to be rounded to the nearest integer. Sometimes a slightly different convenient value produces a much faster and equally reliable calculation.
3. Analyse the Option Gap Before Calculating
One of the most important estimation skills is to examine the answer choices before deciding how accurate your calculation must be.
Decision Rule:
• Options very far apart → rough estimation may be enough.
• Options moderately separated → retain one extra level of accuracy.
• Options very close → use precise calculation or a highly accurate shortcut.
Example:
Suppose an estimated answer is around 200.
Options: 100, 200, 300, 400
→ A rough estimate is enough.
Options: 198, 200, 202, 204
→ Rough estimation is not enough.
Exam Tip:
Do not spend time calculating more accurately than the options require.
4. Compatible Numbers
Compatible numbers are nearby values that work together to make arithmetic easy, especially in multiplication and division.
Example:
598 ÷ 29.9
Choose compatible values:
598 ≈ 600
29.9 ≈ 30
600÷30 = 20.
Example:
398×24.9
398 ≈ 400
24.9 ≈ 25
400×25 = 10,000.
Shortcut:
Useful compatible pairs include:
600÷30, 800÷40, 1000÷25, 720÷18, 480÷24 and 400×25.
5. Order-of-Magnitude Check
Before detailed calculation, determine the approximate size of the answer. This quickly eliminates impossible options.
Example:
198×51
This is approximately:
200×50 = 10,000.
Therefore an option such as 1,000 or 100,000 can immediately be rejected.
Key Principle:
First estimate whether the answer should be in tens, hundreds, thousands or lakhs. Then refine only if necessary.
Exam Trap:
A misplaced decimal point can produce an answer of the wrong order of magnitude. A quick size check often catches such errors instantly.
6. Estimation in Addition and Subtraction
Addition and subtraction can often be estimated by grouping nearby round numbers.
Example:
198.7 + 301.4 − 99.8
≈199 + 301 −100
≈400.
Shortcut:
Look for pairs that approximately make 100, 500, 1000 or another convenient round total.
Observation:
When one number is rounded upward and another downward, the errors may partially cancel.
7. Balanced Estimation in Multiplication
In multiplication, rounding both factors in the same direction may sometimes exaggerate the error. Balanced estimation can produce a closer result.
Example:
49.8×20.2
49.8≈50
20.2≈20
50×20=1000.
Observation:
One factor is rounded upward and the other downward. Their errors partly compensate for each other.
Exam Tip:
Do not deliberately force balanced rounding if it makes the numbers inconvenient. Accuracy and simplicity should both improve.
8. Ratio-Preserving Estimation in Division
Division requires special care because changing the denominator can noticeably change the quotient. Choose numerator and denominator values that preserve the approximate ratio.
Example:
799 ÷ 39.8
799≈800
39.8≈40
800÷40=20.
Exam Method:
For a/b, try to replace both a and b by nearby compatible numbers rather than rounding only one of them heavily.
Exam Trap:
Rounding a small denominator too aggressively can create a large error in the quotient.
9. Percentage Estimation
Percentages close to familiar fractions can be estimated very quickly.
Useful Equivalents:
50% = 1/2
25% = 1/4
20% = 1/5
12.5% = 1/8
75% = 3/4
33⅓% ≈ 1/3
Example:
Find approximately 24.9% of 803.
24.9%≈25%
803≈800
25% of 800
=800/4
=200.
Shortcut:
Whenever the percentage is near a familiar fraction, convert it mentally instead of multiplying by the decimal percentage.
10. Estimation Using Algebraic Identities
An estimation question does not always require numerical rounding. Sometimes an exact algebraic identity reduces the expression first, after which only a small approximation is needed.
Useful Identity:
(a+b)2 − (a−b)2 = 4ab
Example:
Estimate:
(2.7+0.5)2 − (2.7−0.5)2
Using the identity:
=4×2.7×0.5
=2×2.7
=5.4.
Exam Shortcut:
Before rounding a complicated expression, check whether factorisation or an identity can simplify it exactly.
11. Using Upper and Lower Bounds
Sometimes you do not need a single estimated value. It is enough to show that the exact answer lies inside a narrow interval containing only one option.
Example:
Suppose a product is clearly greater than 490 and less than 510.
Options: 420, 500, 580, 650.
Only 500 lies in the reasonable range.
Nearest-Value Strategy:
Establishing a reliable range can be faster than calculating a central estimate.
Exam Tip:
This method is especially useful when answer choices are widely spaced.
12. Direction of Approximation Error
Knowing whether your estimate is slightly high or slightly low helps you choose between nearby options.
Example:
19.8×20.1
Using 20×20 gives 400.
Since one factor is below 20 and the other only slightly above 20, the exact value will be very close to 400.
Observation:
If every positive factor has been rounded upward, the estimated product will usually be above the exact product. If all have been rounded downward, it will usually be below it.
Exam Tip:
Error direction is a useful tie-breaker when two options are close to the estimated result.
13. Two-Stage Estimation
A fast exam technique is to begin with a rough estimate and refine it only if necessary.
Two-Stage Method:
Stage 1: Use rough compatible values.
Stage 2: If two options remain possible, retain one additional digit or use a better nearby value.
Example:
149.6×4.02÷19.9
First estimate:
150×4÷20 = 30.
If options are 10, 20, 30 and 50, stop here.
If options are 29.8, 30.0, 30.2 and 30.4, more accurate calculation is required.
14. Nearest-Option Elimination
In many MCQs, it is faster to eliminate impossible options than to calculate a highly accurate answer.
Example:
Approximately evaluate 199.6×5.1.
≈200×5 = 1000.
Options:
A. 98
B. 510
C. 1018
D. 10,200
Only 1018 is of the correct size and reasonably close.
Exam Shortcut:
Use magnitude, sign and approximate value together to eliminate choices.
15. When Exact Calculation is Better
Estimation is not always the best method. Some expressions become exact immediately through cancellation, factorisation or a familiar identity.
Example:
(59.92−40.12)/(59.9+40.1)
Using a2−b2=(a−b)(a+b):
The denominator cancels.
=59.9−40.1
=19.8.
Exam Tip:
Do not approximate a calculation that can be simplified exactly in fewer steps.
16. Mixed-Expression Estimation
When addition, subtraction, multiplication and division appear together, approximate the numbers first where appropriate, but still follow BODMAS.
Example:
24.8÷5.1 + 9.9×3.05
≈25÷5 + 10×3
=5+30
=35.
Common Mistake:
Approximation changes the numbers, not the order of operations. BODMAS remains valid.
17. Fast Exam Strategy
Step-by-Step Method:
1. Confirm that estimation is appropriate.
2. Look at the option gap.
3. Check the expected order of magnitude.
4. Search for identities, cancellation or factorisation first.
5. Choose compatible nearby numbers.
6. Preserve ratios carefully in division.
7. Apply BODMAS.
8. Compare the estimate with the options.
9. Note whether the estimate is likely high or low.
10. Refine only if two options remain possible.
18. Common Exam Traps
Trap 1:
Using a very rough estimate when the options are close.
Trap 2:
Rounding every number independently without looking for compatible pairs.
Trap 3:
Ignoring the denominator's sensitivity in division.
Trap 4:
Ignoring an exact identity and performing unnecessary approximation.
Trap 5:
Choosing the numerically nearest option without checking sign or magnitude.
Trap 6:
Forgetting BODMAS after replacing values by estimates.
Trap 7:
Assuming greater accuracy is always better. In a timed exam, unnecessary precision wastes time.
19. Quick Revision
Remember:
• Estimation should be accurate enough to identify the correct option.
• Study the option gap before choosing the level of precision.
• Use compatible numbers for multiplication and division.
• First check the order of magnitude.
• Balanced rounding can reduce multiplication error.
• Preserve the approximate ratio in division.
• Use familiar percentage-fraction equivalents.
• Look for identities before doing numerical approximation.
• A reliable upper-lower range may be enough.
• Know whether your estimate is likely high or low.
• Use two-stage estimation when options are close.
• Exact simplification is better than approximation when it is shorter.
• BODMAS still applies after estimation.
20. Verified Previous-Year Questions
RRB Group D PYQ
Nearest-Value Estimation
30 September 2022 · Shift I
Q1. Find the closest approximate value of: 2.33 − 4.12 + 6.13 × 11.3
A. 106
B. 64
C. 39
D. 43
Correct Answer: B. 64
Use convenient nearby values:
2.33≈2
4.12≈4
6.13≈6
11.3≈11.
Therefore:
2−4+6×11
=2−4+66
=64.
RRB Group D PYQ
Compatible Numbers
26 August 2022 · Shift I
Q2. Find the closest approximate value of: 44.999 ÷ 8.998 + 23.996 ÷ 11.998 − 7.009 + 8.002 × 1.998
A. 28
B. 16
C. 20
D. 24
Correct Answer: B. 16
Approximate:
44.999≈45
8.998≈9
23.996≈24
11.998≈12
7.009≈7
8.002≈8
1.998≈2.
Then:
45÷9 + 24÷12 −7 +8×2
=5+2−7+16
=16.
RRB Group D PYQ
Nearest-Option Method
15 September 2022 · Shift II
Q3. Find the closest approximate value of: 17.99 − 16.02 + 19.89 × 8.19
A. 122
B. 330
C. 42
D. 162
Correct Answer: D. 162
17.99≈18
16.02≈16
19.89≈20
8.19≈8.
Therefore:
18−16+20×8
=2+160
=162.
RRB NTPC PYQ
Identity & Estimation
8 January 2021 · CBT-I · Shift I
Q4. Find the approximate value of: (2.697 + 0.498)2 − (2.697 − 0.498)2
A. 2.00
B. 5.37
C. 2.199
D. 3.195
Correct Answer: B. 5.37
Use:
(a+b)2−(a−b)2=4ab.
Therefore:
=4×2.697×0.498
=5.372424.
Approximate value = 5.37.
21. Practice MCQs
Practice MCQ
Q1. Find the nearest approximate value of 49.6 × 20.3.
A. 800
B. 900
C. 1000
D. 1100
Correct Answer: C. 1000
49.6≈50 and 20.3≈20. Therefore 50×20=1000.
Practice MCQ
Q2. Estimate: 198.4 + 301.2 − 99.7.
A. 350
B. 400
C. 450
D. 500
Correct Answer: B. 400
198.4≈200, 301.2≈300 and 99.7≈100. Therefore 200+300−100=400.
Practice MCQ
Q3. Find the nearest value of 799 ÷ 39.8.
A. 10
B. 20
C. 30
D. 40
Correct Answer: B. 20
799≈800 and 39.8≈40. Therefore 800÷40=20.
Practice MCQ
Q4. Estimate: 24.8 ÷ 5.1 + 9.9 × 3.05.
A. 30
B. 35
C. 40
D. 45
Correct Answer: B. 35
24.8≈25, 5.1≈5, 9.9≈10 and 3.05≈3. Hence 25÷5+10×3=5+30=35.
Practice MCQ
Q5. Approximately find 49.8% of 200.6.
A. 80
B. 90
C. 100
D. 120
Correct Answer: C. 100
49.8%≈50% and 200.6≈200. Half of 200=100.
Practice MCQ
Q6. Find the closest value of 19.82.
A. 360
B. 380
C. 400
D. 420
Correct Answer: C. 400
19.8≈20. Hence 19.8² is close to 20²=400. The exact value is 392.04, whose nearest option is 400.
Practice MCQ
Q7. Find the nearest value of (59.92−40.12) ÷ (59.9+40.1).
A. 18
B. 20
C. 22
D. 25
Correct Answer: B. 20
Using a²−b²=(a−b)(a+b), the denominator cancels. Value=59.9−40.1=19.8, whose nearest option is 20.
Practice MCQ
Q8. Approximately evaluate: 149.6 × 4.02 ÷ 19.9.
A. 20
B. 25
C. 30
D. 35
Correct Answer: C. 30
149.6≈150, 4.02≈4 and 19.9≈20. Therefore 150×4÷20=600÷20=30.
Practice MCQ
Q9. Approximately find 24.9% of 803.
A. 180
B. 190
C. 200
D. 220
Correct Answer: C. 200
24.9%≈25% and 803≈800. Therefore 25% of 800=800/4=200.
Practice MCQ
Q10. Estimate: (399.2 + 201.7) ÷ 30.1.
A. 15
B. 18
C. 20
D. 24
Correct Answer: C. 20
399.2+201.7≈400+200=600 and 30.1≈30. Therefore 600÷30=20.
1. Estimation क्या है?
Estimation अर्थात exact answer की पूरी calculation किए बिना उसके sufficiently close value का अनुमान लगाना। Competitive examinations में यह विशेष रूप से nearest-value, approximate-value तथा widely spaced options वाले questions में उपयोगी है।
मुख्य विचार:
Estimation का उद्देश्य random rough answer निकालना नहीं है। Estimated value इतनी accurate होनी चाहिए कि सही option confidently identify किया जा सके।
उदाहरण:
49.7 × 20.1
49.7≈50
20.1≈20
Estimated product≈50×20=1000।
Exam Tip:
Exact calculation लंबी हो और options दूर-दूर हों तो estimation बहुत powerful method है।
2. Rounding, Estimation और Nearest-Value Method
| Method | अर्थ | मुख्य उपयोग |
|---|
| Rounding | Fixed place-value rule के अनुसार nearby value लेना | Nearest integer, ten, decimal place आदि |
| Estimation | Calculation आसान करने के लिए convenient nearby values लेना | Fast calculation |
| Nearest-Value Method | इतना accurate estimate निकालना कि nearest option पहचाना जा सके | MCQ examinations |
Observation:
Nearest-value question में हर number को nearest integer तक round करना जरूरी नहीं है। कभी-कभी अन्य convenient nearby values अधिक useful होती हैं।
3. Calculation से पहले Option Gap देखें
Decision Rule:
• Options बहुत दूर हों → rough estimation पर्याप्त हो सकती है।
• Options moderately close हों → थोड़ी अधिक accuracy रखें।
• Options बहुत close हों → precise calculation या accurate shortcut आवश्यक है।
उदाहरण:
Estimated answer लगभग 200 है।
Options: 100, 200, 300, 400
→ Rough estimate पर्याप्त है।
Options: 198, 200, 202, 204
→ Rough estimate पर्याप्त नहीं है।
Exam Tip:
Options जितनी accuracy require करें, calculation उतनी ही करें। Unnecessary precision समय खराब करती है।
4. Compatible Numbers
Compatible numbers ऐसे nearby values होते हैं जिनके साथ multiplication या division बहुत आसान हो जाता है।
उदाहरण:
598÷29.9
598≈600
29.9≈30
600÷30=20।
उदाहरण:
398×24.9
398≈400
24.9≈25
400×25=10,000।
Shortcut:
Useful compatible pairs:
600÷30, 800÷40, 1000÷25, 720÷18, 480÷24 तथा400×25।
5. Order-of-Magnitude Check
Detailed calculation से पहले यह अनुमान लगाएँ कि answer tens, hundreds, thousands या किसी अन्य range में होना चाहिए।
उदाहरण:
198×51
लगभग:
200×50=10,000।
इसलिए 1,000 या100,000 जैसे options तुरंत eliminate किए जा सकते हैं।
मुख्य नियम:
पहले answer का approximate size पहचानें, फिर आवश्यकता होने पर precision बढ़ाएँ।
Exam Trap:
Decimal point गलत place पर लगाने की mistake order-of-magnitude check से तुरंत पकड़ी जा सकती है।
6. Addition एवं Subtraction में Estimation
उदाहरण:
198.7 + 301.4 − 99.8
≈199+301−100
≈400।
Shortcut:
100, 500, 1000 या अन्य round total बनाने वाले approximate pairs देखें।
Observation:
एक number ऊपर और दूसरा नीचे round होने पर errors आंशिक रूप से cancel हो सकते हैं।
7. Multiplication में Balanced Estimation
उदाहरण:
49.8×20.2
≈50×20
=1000।
Observation:
पहला factor थोड़ा ऊपर और दूसरा थोड़ा नीचे round हुआ है। इससे errors एक सीमा तक balance हो जाते हैं।
Exam Tip:
Balanced rounding तभी उपयोग करें जब convenient calculation और reasonable accuracy दोनों मिलें।
8. Division में Ratio-Preserving Estimation
Division में denominator बदलने से quotient पर अधिक प्रभाव पड़ सकता है। इसलिए numerator और denominator दोनों के compatible nearby values चुनना अधिक सुरक्षित होता है।
उदाहरण:
799÷39.8
799≈800
39.8≈40
800÷40=20।
Exam Method:
a/b में numerator और denominator दोनों को ऐसे nearby values में बदलें जिससे approximate ratio बना रहे और division आसान हो जाए।
Exam Trap:
Small denominator को बहुत aggressively round करने पर quotient में बड़ा error आ सकता है।
9. Percentage Estimation
Useful Equivalents:
50%=1/2
25%=1/4
20%=1/5
12.5%=1/8
75%=3/4
33⅓%≈1/3
उदाहरण:
24.9% of 803 का approximate value ज्ञात करें।
24.9%≈25%
803≈800
25% of800
=800/4
=200।
Shortcut:
Percentage familiar fraction के पास हो तो decimal multiplication के बजाय fraction equivalent use करें।
10. Algebraic Identities द्वारा Estimation
हर estimation question में direct rounding करना आवश्यक नहीं है। पहले exact identity से expression छोटा करना अधिक efficient हो सकता है।
Useful Identity:
(a+b)2−(a−b)2=4ab
उदाहरण:
(2.7+0.5)2−(2.7−0.5)2
=4×2.7×0.5
=2×2.7
=5.4।
Exam Shortcut:
Complicated numbers को round करने से पहले factorisation या identity की possibility देखें।
11. Upper एवं Lower Bounds का प्रयोग
कभी exact estimated value निकालने की आवश्यकता नहीं होती। यदि यह सिद्ध हो जाए कि answer एक narrow range में है और उस range में केवल एक option है, तो वही correct choice होगी।
उदाहरण:
यदि answer clearly 490 से अधिक और510 से कम है।
Options: 420, 500, 580, 650
तो केवल 500 reasonable option है।
Nearest-Value Strategy:
Reliable range निकालना कई बार central estimate निकालने से भी तेज होता है।
12. Approximation Error की Direction
Estimate exact answer से थोड़ा ऊपर है या नीचे, यह समझने से nearby options के बीच सही choice करना आसान होता है।
उदाहरण:
19.8×20.1
20×20=400 एक अच्छा estimate है।
Exact value भी 400 के बहुत close होगी।
Observation:
Positive factors सभी ऊपर round किए गए हों तो estimated product generally exact product से ऊपर होगा। सभी नीचे round हों तो estimate generally नीचे होगा।
Exam Tip:
दो options estimated answer के आसपास हों तो error direction tie-breaker की तरह उपयोगी हो सकती है।
13. Two-Stage Estimation
Two-Stage Method:
Stage 1: Rough compatible values लेकर जल्दी estimate निकालें।
Stage 2: यदि दो options possible रहें तो एक अतिरिक्त digit retain करके calculation refine करें।
उदाहरण:
149.6×4.02÷19.9
Rough estimate:
150×4÷20=30।
Options 10, 20, 30, 50 हों तो यहीं stop करें।
Options 29.8, 30.0, 30.2, 30.4 हों तो अधिक precise calculation करें।
14. Nearest-Option Elimination
उदाहरण:
199.6×5.1
≈200×5
≈1000।
Options:
A. 98
B. 510
C. 1018
D. 10,200
सिर्फ 1018 correct magnitude और nearest range में है।
Exam Shortcut:
Magnitude, sign और approximate value—तीनों को मिलाकर options eliminate करें।
15. कब Exact Calculation बेहतर है?
यदि cancellation, factorisation या identity से expression तुरंत exact simplify हो सकता है तो approximation लगाने की आवश्यकता नहीं है।
उदाहरण:
(59.92−40.12)/(59.9+40.1)
a2−b2=(a−b)(a+b)
Denominator cancel होगा।
=59.9−40.1
=19.8।
Exam Tip:
जो calculation exact shortcut से कम steps में हो सकती है, उसे unnecessarily approximate न करें।
16. Mixed Expressions में Estimation
उदाहरण:
24.8÷5.1 + 9.9×3.05
≈25÷5 + 10×3
=5+30
=35।
सामान्य गलती:
Approximation केवल numbers बदलती है, operations का mathematical order नहीं। BODMAS हमेशा लागू रहेगा।
17. Fast Exam Strategy
Step-by-Step Method:
1. देखें estimation appropriate है या नहीं।
2. Options का gap देखें।
3. Expected magnitude पहचानें।
4. Identity, cancellation या factorisation पहले देखें।
5. Compatible nearby values चुनें।
6. Division में approximate ratio preserve करें।
7. BODMAS apply करें।
8. Estimate को options से compare करें।
9. देखें estimate थोड़ा high है या low।
10. आवश्यकता होने पर ही calculation refine करें।
18. Common Exam Traps
Trap 1:
Close options के बावजूद बहुत rough estimate use करना।
Trap 2:
Compatible pairs देखे बिना हर number independently round करना।
Trap 3:
Division में denominator sensitivity ignore करना।
Trap 4:
Exact identity उपलब्ध होने के बावजूद unnecessary approximation करना।
Trap 5:
Sign और magnitude check किए बिना केवल numerically nearest option चुनना।
Trap 6:
Estimation के बाद BODMAS भूल जाना।
Trap 7:
यह मान लेना कि अधिक precision हमेशा बेहतर है। Timed examination में unnecessary precision समय waste करती है।
19. Quick Revision
एक नज़र में:
• Estimate इतना accurate हो कि correct option identify हो सके।
• Precision तय करने से पहले option gap देखें।
• Multiplication/division में compatible numbers उपयोग करें।
• सबसे पहले order of magnitude check करें।
• Balanced rounding multiplication error कम कर सकती है।
• Division में approximate ratio preserve करें।
• Familiar percentage-fraction equivalents use करें।
• Numerical approximation से पहले identities देखें।
• कई questions में upper-lower range पर्याप्त होती है।
• Estimate high है या low, यह समझें।
• Close options में two-stage estimation use करें।
• Exact shortcut छोटा हो तो approximation से बेहतर है।
• Estimation के बाद भी BODMAS follow करें।
20. Verified Previous-Year Questions
RRB Group D PYQ
Nearest-Value Estimation
30 सितंबर 2022 · Shift I
प्रश्न 1. 2.33 − 4.12 + 6.13 × 11.3 का closest approximate value ज्ञात करें।
A. 106
B. 64
C. 39
D. 43
सही उत्तर: B. 64
2.33≈2
4.12≈4
6.13≈6
11.3≈11।
अतः:
2−4+6×11
=2−4+66
=64।
RRB Group D PYQ
Compatible Numbers
26 अगस्त 2022 · Shift I
प्रश्न 2. 44.999 ÷ 8.998 + 23.996 ÷ 11.998 − 7.009 + 8.002 × 1.998 का closest approximate value ज्ञात करें।
A. 28
B. 16
C. 20
D. 24
सही उत्तर: B. 16
44.999≈45
8.998≈9
23.996≈24
11.998≈12
7.009≈7
8.002≈8
1.998≈2।
अब:
45÷9+24÷12−7+8×2
=5+2−7+16
=16।
RRB Group D PYQ
Nearest-Option Method
15 सितंबर 2022 · Shift II
प्रश्न 3. 17.99 − 16.02 + 19.89 × 8.19 का closest approximate value ज्ञात करें।
A. 122
B. 330
C. 42
D. 162
सही उत्तर: D. 162
17.99≈18
16.02≈16
19.89≈20
8.19≈8।
अतः:
18−16+20×8
=2+160
=162।
RRB NTPC PYQ
Identity & Estimation
8 जनवरी 2021 · CBT-I · Shift I
प्रश्न 4. (2.697 + 0.498)2 − (2.697 − 0.498)2 का approximate value ज्ञात करें।
A. 2.00
B. 5.37
C. 2.199
D. 3.195
सही उत्तर: B. 5.37
Identity:
(a+b)2−(a−b)2=4ab।
अतः:
4×2.697×0.498
=5.372424।
Approximate value=5.37।
21. Practice MCQs
Practice MCQ
प्रश्न 1. 49.6 × 20.3 का nearest approximate value ज्ञात करें।
A. 800
B. 900
C. 1000
D. 1100
सही उत्तर: C. 1000
49.6≈50 तथा20.3≈20। इसलिए 50×20=1000।
Practice MCQ
प्रश्न 2. 198.4 + 301.2 − 99.7 का estimate ज्ञात करें।
A. 350
B. 400
C. 450
D. 500
सही उत्तर: B. 400
198.4≈200, 301.2≈300 तथा99.7≈100। इसलिए 200+300−100=400।
Practice MCQ
प्रश्न 3. 799 ÷ 39.8 का nearest value ज्ञात करें।
A. 10
B. 20
C. 30
D. 40
सही उत्तर: B. 20
799≈800 और39.8≈40। इसलिए 800÷40=20।
Practice MCQ
प्रश्न 4. 24.8 ÷ 5.1 + 9.9 × 3.05 का estimate ज्ञात करें।
A. 30
B. 35
C. 40
D. 45
सही उत्तर: B. 35
24.8≈25, 5.1≈5, 9.9≈10 तथा3.05≈3। इसलिए 25÷5+10×3=5+30=35।
Practice MCQ
प्रश्न 5. 49.8% of 200.6 का approximate value ज्ञात करें।
A. 80
B. 90
C. 100
D. 120
सही उत्तर: C. 100
49.8%≈50% तथा200.6≈200। 200 का आधा=100।
Practice MCQ
प्रश्न 6. 19.82 का closest value ज्ञात करें।
A. 360
B. 380
C. 400
D. 420
सही उत्तर: C. 400
19.8≈20। अतः 19.8² लगभग20²=400 है। Exact value392.04 है, जिसका nearest option400 है।
Practice MCQ
प्रश्न 7. (59.92−40.12) ÷ (59.9+40.1) का nearest value ज्ञात करें।
A. 18
B. 20
C. 22
D. 25
सही उत्तर: B. 20
a²−b²=(a−b)(a+b)। Denominator cancel होगा। Value=59.9−40.1=19.8। इसका nearest option=20।
Practice MCQ
प्रश्न 8. 149.6 × 4.02 ÷ 19.9 का approximate value ज्ञात करें।
A. 20
B. 25
C. 30
D. 35
सही उत्तर: C. 30
149.6≈150, 4.02≈4 तथा19.9≈20। इसलिए 150×4÷20=600÷20=30।
Practice MCQ
प्रश्न 9. 24.9% of 803 का approximate value ज्ञात करें।
A. 180
B. 190
C. 200
D. 220
सही उत्तर: C. 200
24.9%≈25% तथा803≈800। इसलिए 800 का25%=800/4=200।
Practice MCQ
प्रश्न 10. (399.2 + 201.7) ÷ 30.1 का estimate ज्ञात करें।
A. 15
B. 18
C. 20
D. 24
सही उत्तर: C. 20
399.2+201.7≈400+200=600 तथा30.1≈30। इसलिए 600÷30=20।