1. What is Approximation?
Approximation means replacing an exact value by a nearby value that is easier to understand or calculate with. In competitive examinations, approximation is especially useful when the options are sufficiently far apart and an exact calculation would consume unnecessary time.
Key Idea:
An approximate value should be close enough to the exact value for the purpose of the question while making the calculation substantially easier.
Example:
49.92 ≈ 50
199.7 ≈ 200
3.98 ≈ 4
Exam Tip:
Do not approximate merely because decimals appear. If the options are very close, exact or more accurate calculation may be necessary.
2. Approximation and Rounding Off
Rounding off is a systematic method of approximation. A number is replaced by the nearest value at a specified place such as units, tens, hundreds or decimal places.
Important Difference:
Rounding off follows a specified place-value rule.
Approximation is broader and may involve replacing several numbers by convenient nearby values for faster calculation.
Example:
47.68 rounded to the nearest integer = 48.
For a quick approximate calculation, 47.68 may also be treated as about 50 if that level of accuracy is sufficient.
3. Basic Rule of Rounding
To round a number, first identify the digit that must be retained and then examine the digit immediately to its right.
Rounding Rule:
If the next digit is 0, 1, 2, 3 or 4, keep the retained digit unchanged.
If the next digit is 5, 6, 7, 8 or 9, increase the retained digit by 1.
Example:
64.32 rounded to one decimal place:
Retained digit = 3
Next digit = 2
Therefore answer = 64.3.
Example:
64.38 rounded to one decimal place:
Retained digit = 3
Next digit = 8
Therefore answer = 64.4.
4. Rounding to the Nearest Integer
To round a decimal number to the nearest integer, examine the first digit after the decimal point.
Example:
27.43 → 27
because the tenths digit is 4.
Example:
27.76 → 28
because the tenths digit is 7.
Key Rule:
For nearest-integer rounding:
Decimal part < 0.5 → lower integer
Decimal part ≥ 0.5 → next integer
5. Rounding to Tens, Hundreds and Thousands
The same rule applies to whole numbers. Look at the digit immediately to the right of the required place.
Example — Nearest Ten:
467 → 470
The units digit is 7, so the tens digit increases.
Example — Nearest Hundred:
6,847 → 6,800
The tens digit is 4, so the hundreds digit remains unchanged.
Example — Nearest Thousand:
36,680 → 37,000
The hundreds digit is 6, so the thousands digit increases.
Shortcut:
Mark the required place, inspect only the next digit, and then replace all following whole-number digits by zeros.
6. Rounding Decimal Numbers to Specified Decimal Places
Decimal places are counted from the first digit after the decimal point.
Example — Two Decimal Places:
12.746
Keep 12.74 and inspect the third decimal digit, 6.
Therefore:
12.746 ≈ 12.75.
Example — Three Decimal Places:
8.23547
The fourth decimal digit is 4.
Therefore:
8.23547 ≈ 8.235.
Common Mistake:
Do not count decimal places from the first non-zero digit. Decimal places always begin immediately after the decimal point.
7. Significant Figures
Significant figures measure the meaningful precision of a number. Counting begins from the first non-zero digit.
Key Rules:
• Leading zeros are not significant.
• Zeros between non-zero digits are significant.
• Trailing zeros after a decimal point are significant when explicitly written.
Example:
0.004586 rounded to 3 significant figures:
The first three significant digits are 4, 5 and 8.
The next digit is 6.
Therefore:
0.004586 ≈ 0.00459.
Example:
37,648 rounded to 3 significant figures:
First three significant digits = 3, 7, 6.
Next digit = 4.
Answer = 37,600.
8. Rounding Negative Numbers
The usual school-level competitive-exam rounding rule is applied to the magnitude of the number while retaining its negative sign.
Example:
−7.46 rounded to one decimal place:
7.46 → 7.5
Therefore:
−7.5.
Example:
−12.31 rounded to the nearest integer = −12.
Exam Trap:
Do not confuse rounding with always moving toward zero. The rounded value must be the nearest value at the required precision.
9. Approximation in Addition and Subtraction
For quick addition or subtraction, numbers may be rounded to convenient values of similar precision.
Example:
Approximate:
398.4 + 201.7 + 99.6
≈ 400 + 200 + 100
= 700.
Shortcut:
In addition and subtraction, nearby errors may partly compensate for one another. Round each term sensibly rather than always rounding every number in the same direction.
10. Approximation in Multiplication
Products can often be estimated very quickly when the factors are close to convenient integers or multiples of 10.
Example:
49.8 × 20.2
≈ 50×20
= 1000.
Example:
9.96 × 30.1
≈ 10×30
= 300.
Exam Tip:
Multiplication can magnify rounding errors. Avoid excessive rounding when the answer options are close together.
11. Approximation in Division
In division, try to round the dividend and divisor so that they form an easy quotient.
Example:
598 ÷ 29.9
≈ 600÷30
= 20.
Shortcut:
Look for nearby compatible numbers such as:
600÷30, 480÷24, 1000÷25, 720÷18.
Exam Trap:
Do not round the divisor too aggressively when it is small. Even a small change in the divisor can noticeably affect the quotient.
12. Approximation with Percentages
Percentages close to familiar values such as 10%, 20%, 25%, 33⅓%, 50% or 75% can often simplify an approximate calculation.
Example:
Approximately find 24.9% of 401.
24.9% ≈ 25%
401 ≈ 400
25% of 400
= 1/4×400
= 100.
Exam Shortcut:
Recognise familiar percentage-fraction pairs:
25% = 1/4
50% = 1/2
75% = 3/4
20% = 1/5
12.5% = 1/8
13. Balanced Rounding
Good approximation does not always mean rounding every value to the nearest integer independently. Sometimes slightly different convenient values provide a cleaner calculation while keeping the overall error small.
Example:
199.8 × 5.02
A very convenient approximation is:
200×5 = 1000.
Observation:
One factor has been rounded slightly upward and the other slightly downward. Such balanced rounding can reduce the overall error.
Exam Tip:
Use balanced rounding only when the question asks for an approximate or nearest value. For an exact-value question, do not replace given values arbitrarily.
14. Avoiding Excessive Rounding
Each approximation introduces some error. If several numbers are rounded too heavily, the combined error may shift the result toward the wrong option.
Example of Poor Approximation:
Suppose an answer is near 54 and the options are 52, 54, 56 and 58.
Rounding every term very aggressively may produce 50 or 60 and lead to the wrong option.
Better Strategy:
• Wide option gap → rough approximation is usually enough.
• Narrow option gap → retain more digits.
• Exact-value question → calculate exactly unless a mathematically exact shortcut exists.
15. Error Range in Rounding
When a value is rounded to a certain unit, the maximum rounding error is half of that unit.
Key Rule:
Rounded to nearest 1 → maximum error = 0.5
Rounded to nearest 10 → maximum error = 5
Rounded to nearest 100 → maximum error = 50
Rounded to nearest 0.1 → maximum error = 0.05
Example:
If a number rounded to the nearest 10 is 350, the original value lies approximately from 345 up to, but not including, 355.
Observation:
This concept explains why excessive rounding can become dangerous in long calculations.
16. Fast Exam Method
Step-by-Step Method:
1. Check whether the question asks for an exact or approximate value.
2. Observe how far apart the options are.
3. Round numbers to convenient values while retaining sufficient accuracy.
4. Apply BODMAS to the rounded expression.
5. Compare the estimated result with the options.
6. If two options remain close, recalculate using one extra digit of precision.
Exam Tip:
Options are part of the approximation strategy. A calculation need only be accurate enough to identify the correct option confidently.
17. Common Exam Traps
Trap 1:
Applying rounding when the question asks for an exact answer.
Trap 2:
Using the wrong digit to decide whether to round up or down.
Trap 3:
Confusing decimal places with significant figures.
Trap 4:
Rounding every value too aggressively when options are close.
Trap 5:
Ignoring BODMAS after numbers have been approximated.
Trap 6:
Assuming an approximate answer must equal the rounded value of every individual term. Convenient balanced approximation may sometimes be better.
Trap 7:
Forgetting that negative values are also rounded according to their nearest required place value.
18. Quick Revision
Remember:
• Approximation replaces an exact value with a nearby convenient value.
• Rounding off is a systematic form of approximation.
• Next digit 0–4 → retain the digit.
• Next digit 5–9 → increase the retained digit by 1.
• For nearest integer, inspect the tenths digit.
• For nearest ten, inspect the units digit.
• For nearest hundred, inspect the tens digit.
• Decimal places begin immediately after the decimal point.
• Significant figures begin from the first non-zero digit.
• Use compatible numbers for multiplication and division.
• Use familiar percentage-fraction equivalents.
• Wide option gap permits rougher approximation.
• Close options require greater precision.
• Always apply BODMAS even after rounding.
19. Verified Previous-Year Questions
RRB Group D PYQ
Approximation
5 September 2022 · Shift I
Q1. Find the closest approximate value of: 4.49 ÷ 1.49 − 3.33 × 3 + 4.49
A. −2.5
B. −4.5
C. 4.5
D. 2.5
Correct Answer: A. −2.5
Use convenient approximations:
4.49÷1.49 ≈ 3
3.33×3 ≈ 10
Therefore:
3−10+4.49
≈ −2.51
Closest option = −2.5.
SSC MTS PYQ
Approximate Division & Multiplication
6 July 2022 · Shift III
Q2. Find the approximate value of: 305.03 ÷ 61.09 × 11.47
A. 57
B. 47
C. 12
D. 63
Correct Answer: A. 57
305.03÷61.09 is approximately 5.
So the expression is approximately:
5×11.47
≈57.35.
The nearest available option is 57.
RRB NTPC PYQ
Approximation with Powers
17 June 2022 · CBT-II Level 3 · Shift III
Q3. Find the closest approximate value of: 5.01 + (3.01 × 1.992) × 4 + 6.01 ÷ 2.03
A. 56
B. 65
C. 57
D. 52
Correct Answer: A. 56
Approximate:
5.01≈5
3.01≈3
1.99≈2
6.01≈6
2.03≈2.
Therefore:
5 + (3×22)×4 + 6÷2
=5+12×4+3
=5+48+3
=56.
RRB NTPC PYQ
Percentage Approximation
16 June 2022 · CBT-II Level 2 · Shift I
Q4. Find the closest value of ? in: 44.97% of 226 + 55.03 × 4.98 − ? = 140
A. 25
B. 237
C. 508
D. 120
Correct Answer: B. 237
44.97% ≈45%
55.03≈55
4.98≈5.
Therefore:
45% of 226 + 55×5 − ? ≈140.
45% of 226 ≈102
55×5=275.
So:
102+275−?=140
377−140≈?
?≈237.
20. Practice MCQs
Practice MCQ
Q1. Round 47.68 to the nearest integer.
A. 46
B. 47
C. 48
D. 49
Correct Answer: C. 48
The tenths digit is 6, so 47 is rounded upward to 48.
Practice MCQ
Q2. Round 6,847 to the nearest hundred.
A. 6,700
B. 6,800
C. 6,900
D. 7,000
Correct Answer: B. 6,800
The tens digit is 4, so the hundreds digit remains 8. Answer = 6,800.
Practice MCQ
Q3. Round 12.746 to two decimal places.
A. 12.74
B. 12.75
C. 12.76
D. 12.70
Correct Answer: B. 12.75
The third decimal digit is 6, so 12.74 rounds upward to 12.75.
Practice MCQ
Q4. Round 0.007846 to three significant figures.
A. 0.00784
B. 0.00785
C. 0.00780
D. 0.00800
Correct Answer: B. 0.00785
The first three significant digits are 7, 8 and 4. The next digit is 6, so 4 increases to 5. Answer = 0.00785.
Practice MCQ
Q5. Approximately evaluate: 398.6 + 201.3.
A. 500
B. 550
C. 600
D. 650
Correct Answer: C. 600
398.6≈400 and 201.3≈200. Therefore approximate sum = 600.
Practice MCQ
Q6. Approximately evaluate: 49.8 × 20.2.
A. 500
B. 800
C. 1000
D. 1200
Correct Answer: C. 1000
49.8≈50 and 20.2≈20. Hence 50×20=1000.
Practice MCQ
Q7. Approximately evaluate: 598 ÷ 29.9.
A. 10
B. 20
C. 30
D. 40
Correct Answer: B. 20
598≈600 and 29.9≈30. Therefore 600÷30=20.
Practice MCQ
Q8. Round −7.46 to one decimal place.
A. −7.4
B. −7.5
C. −8.0
D. −7.0
Correct Answer: B. −7.5
The hundredths digit is 6, so the tenths digit increases. Therefore −7.46 rounds to −7.5.
Practice MCQ
Q9. Approximately find 24.6% of 399.8.
A. 80
B. 90
C. 100
D. 120
Correct Answer: C. 100
24.6%≈25% and 399.8≈400. Therefore 25% of 400=100.
Practice MCQ
Q10. Approximately evaluate: 999.4 + 502.6 − 201.9.
A. 1200
B. 1250
C. 1300
D. 1400
Correct Answer: C. 1300
999.4≈999, 502.6≈503 and 201.9≈202. Thus 999+503−202=1300.
1. Approximation क्या है?
Approximation अर्थात किसी exact value के स्थान पर उसके निकट ऐसी value लेना जिससे calculation आसान हो जाए। Competitive examinations में approximation विशेष रूप से तब उपयोगी होती है जब options के बीच पर्याप्त अंतर हो और exact calculation में अनावश्यक समय लगे।
मुख्य विचार:
Approximate value इतनी निकट होनी चाहिए कि question का सही option identify किया जा सके और calculation substantially आसान हो जाए।
उदाहरण:
49.92 ≈ 50
199.7 ≈ 200
3.98 ≈ 4
Exam Tip:
केवल decimals दिखाई देने के कारण approximation न करें। Options बहुत close हों तो अधिक accurate या exact calculation आवश्यक हो सकती है।
2. Approximation और Rounding Off
Rounding off approximation का systematic method है। किसी number को units, tens, hundreds या specified decimal place के nearest value में बदला जाता है।
महत्वपूर्ण अंतर:
Rounding off specified place-value rule के अनुसार किया जाता है।
Approximation broader concept है जिसमें fast calculation के लिए कई numbers को convenient nearby values में बदला जा सकता है।
उदाहरण:
47.68 को nearest integer तक round करने पर 48 मिलेगा।
लेकिन rough calculation में आवश्यकता के अनुसार इसे लगभग 50 भी माना जा सकता है।
3. Rounding का Basic Rule
Rounding Rule:
अगला digit 0, 1, 2, 3 या 4 हो → retained digit unchanged रहेगा।
अगला digit 5, 6, 7, 8 या 9 हो → retained digit में 1 जोड़ें।
उदाहरण:
64.32 को one decimal place तक round करें।
Retained digit = 3
Next digit = 2
Answer = 64.3।
उदाहरण:
64.38 को one decimal place तक round करें।
Next digit 8 है।
Answer = 64.4।
4. Nearest Integer तक Rounding
Decimal number को nearest integer तक round करने के लिए decimal point के बाद पहला digit अर्थात tenths digit देखें।
उदाहरण:
27.43 → 27।
उदाहरण:
27.76 → 28।
मुख्य नियम:
Decimal part < 0.5 → lower integer
Decimal part ≥ 0.5 → next integer
5. Nearest Tens, Hundreds एवं Thousands तक Rounding
Nearest Ten:
467 → 470
Units digit 7 है।
Nearest Hundred:
6,847 → 6,800
Tens digit 4 है।
Nearest Thousand:
36,680 → 37,000
Hundreds digit 6 है।
Shortcut:
Required place को identify करें, केवल उसके तुरंत बाद वाला digit देखें और उसके बाद के whole-number digits को zero कर दें।
6. Specified Decimal Places तक Rounding
Decimal places की counting decimal point के तुरंत बाद वाले digit से शुरू होती है।
उदाहरण — Two Decimal Places:
12.746
Third decimal digit = 6
अतः:
12.746 ≈ 12.75।
उदाहरण — Three Decimal Places:
8.23547
Fourth decimal digit = 4
अतः:
8.23547 ≈ 8.235।
सामान्य गलती:
Decimal places की counting first non-zero digit से नहीं होती। यह decimal point के तुरंत बाद से शुरू होती है।
7. Significant Figures
Significant figures की counting first non-zero digit से शुरू होती है।
मुख्य Rules:
• Starting के leading zeros significant नहीं होते।
• Non-zero digits के बीच के zeros significant होते हैं।
• Decimal के बाद explicitly लिखे trailing zeros precision दर्शा सकते हैं।
उदाहरण:
0.004586 को 3 significant figures तक round करें।
पहले three significant digits = 4, 5, 8।
Next digit = 6।
Answer = 0.00459।
उदाहरण:
37,648 को 3 significant figures तक round करें।
Answer = 37,600।
8. Negative Numbers का Rounding
Competitive-exam level पर सामान्य rounding rule number के magnitude पर लागू किया जाता है और negative sign बनाए रखा जाता है।
उदाहरण:
−7.46 को one decimal place तक round करें।
7.46 → 7.5
अतः answer = −7.5।
उदाहरण:
−12.31 को nearest integer तक round करने पर −12 मिलेगा।
Exam Trap:
Rounding का अर्थ हमेशा zero की ओर जाना नहीं है। Required precision पर nearest value चुननी होती है।
9. Addition एवं Subtraction में Approximation
उदाहरण:
398.4 + 201.7 + 99.6
≈400+200+100
=700।
Shortcut:
Addition/subtraction में numbers को sensible nearby values में round करें। सभी numbers को unnecessarily same direction में round करना आवश्यक नहीं है।
10. Multiplication में Approximation
उदाहरण:
49.8×20.2
≈50×20
=1000।
उदाहरण:
9.96×30.1
≈10×30
=300।
Exam Tip:
Multiplication rounding error को बढ़ा सकती है। Options पास-पास हों तो excessive rounding से बचें।
11. Division में Approximation
उदाहरण:
598÷29.9
≈600÷30
=20।
Shortcut:
ऐसे compatible nearby values खोजें जिनसे division आसान हो, जैसे:
600÷30, 480÷24, 1000÷25, 720÷18।
Exam Trap:
Small divisor को बहुत अधिक round करने पर quotient में significant error आ सकता है।
12. Percentages के साथ Approximation
उदाहरण:
24.9% of 401 का approximate value ज्ञात करें।
24.9%≈25%
401≈400
25% of 400
=400/4
=100।
Exam Shortcut:
25%=1/4
50%=1/2
75%=3/4
20%=1/5
12.5%=1/8
13. Balanced Rounding
हर number को independently nearest integer तक round करना हमेशा best approximation नहीं होता। कभी-कभी convenient nearby values लेने से calculation आसान होती है और overall error भी छोटा रहता है।
उदाहरण:
199.8×5.02
≈200×5
=1000।
Observation:
एक factor थोड़ा ऊपर और दूसरा थोड़ा नीचे round हुआ है। इससे rounding errors एक सीमा तक balance हो सकते हैं।
Exam Tip:
Balanced rounding केवल approximate या nearest-value questions में उपयोग करें। Exact-value question में arbitrary rounding न करें।
14. Excessive Rounding से बचें
प्रत्येक approximation थोड़ा error introduce करती है। कई numbers को बहुत अधिक round करने पर combined error गलत option तक पहुँचा सकती है।
Better Strategy:
• Options में बड़ा gap → rough approximation पर्याप्त हो सकती है।
• Options close हों → अधिक digits retain करें।
• Exact answer पूछा गया हो → exact calculation करें।
Exam Trap:
Nearest-value question में भी calculation को आवश्यकता से अधिक rough न बनाएं।
15. Rounding Error की सीमा
मुख्य नियम:
Nearest 1 तक rounding → maximum error = 0.5
Nearest 10 → maximum error = 5
Nearest 100 → maximum error = 50
Nearest 0.1 → maximum error = 0.05
उदाहरण:
यदि किसी value को nearest 10 तक round करने पर 350 मिलता है, तो original value लगभग 345 से 355 के बीच होगी, जहाँ 355 अगली rounding boundary है।
Observation:
इसी कारण repeated heavy rounding long calculations में dangerous हो सकती है।
16. Fast Exam Method
Step-by-Step Method:
1. देखें question exact value पूछ रहा है या approximate value।
2. Options के बीच gap देखें।
3. पर्याप्त accuracy रखते हुए convenient nearby values चुनें।
4. Rounded expression पर BODMAS लागू करें।
5. Estimated result को options से compare करें।
6. दो options close हों तो एक extra digit retain करके calculation दोबारा करें।
Exam Tip:
Approximation questions में options स्वयं calculation strategy का हिस्सा होते हैं।
17. Common Exam Traps
Trap 1:
Exact-answer question में rounding कर देना।
Trap 2:
गलत digit देखकर round-up या round-down decide करना।
Trap 3:
Decimal places और significant figures को confuse करना।
Trap 4:
Close options के बावजूद numbers को बहुत aggressively round करना।
Trap 5:
Numbers approximate करने के बाद BODMAS भूल जाना।
Trap 6:
यह मान लेना कि हर term को independently nearest integer में ही round करना जरूरी है।
Trap 7:
Negative numbers में nearest-value rule गलत apply करना।
18. Quick Revision
एक नज़र में:
• Approximation exact value के स्थान पर convenient nearby value देता है।
• Rounding off approximation का systematic form है।
• Next digit 0–4 → retained digit unchanged।
• Next digit 5–9 → retained digit +1।
• Nearest integer के लिए tenths digit देखें।
• Nearest ten के लिए units digit देखें।
• Nearest hundred के लिए tens digit देखें।
• Decimal places decimal point के तुरंत बाद से count होते हैं।
• Significant figures first non-zero digit से count होते हैं।
• Multiplication/division में compatible numbers खोजें।
• Familiar percentage-fraction equivalents याद रखें।
• Wide option gap में rough approximation पर्याप्त हो सकती है।
• Close options में अधिक precision रखें।
• Approximation के बाद भी BODMAS follow करें।
19. Verified Previous-Year Questions
RRB Group D PYQ
Approximation
5 सितंबर 2022 · Shift I
प्रश्न 1. 4.49 ÷ 1.49 − 3.33 × 3 + 4.49 का closest approximate value ज्ञात करें।
A. −2.5
B. −4.5
C. 4.5
D. 2.5
सही उत्तर: A. −2.5
4.49÷1.49≈3
3.33×3≈10।
अतः:
3−10+4.49
≈−2.51।
Closest option = −2.5।
SSC MTS PYQ
Approximate Division & Multiplication
6 जुलाई 2022 · Shift III
प्रश्न 2. 305.03 ÷ 61.09 × 11.47 का approximate value ज्ञात करें।
A. 57
B. 47
C. 12
D. 63
सही उत्तर: A. 57
305.03÷61.09 लगभग 5 है।
अतः expression लगभग:
5×11.47
≈57.35।
Nearest available option = 57।
RRB NTPC PYQ
Approximation with Powers
17 जून 2022 · CBT-II Level 3 · Shift III
प्रश्न 3. 5.01 + (3.01 × 1.992) × 4 + 6.01 ÷ 2.03 का closest approximate value ज्ञात करें।
A. 56
B. 65
C. 57
D. 52
सही उत्तर: A. 56
5.01≈5
3.01≈3
1.99≈2
6.01≈6
2.03≈2।
अब:
5+(3×22)×4+6÷2
=5+48+3
=56।
RRB NTPC PYQ
Percentage Approximation
16 जून 2022 · CBT-II Level 2 · Shift I
प्रश्न 4. 44.97% of 226 + 55.03 × 4.98 − ? = 140 में ? का closest value ज्ञात करें।
A. 25
B. 237
C. 508
D. 120
सही उत्तर: B. 237
44.97%≈45%
55.03≈55
4.98≈5।
45% of 226 ≈102
55×5=275।
अतः:
102+275−?=140
?≈377−140
=237।
20. Practice MCQs
Practice MCQ
प्रश्न 1. 47.68 को nearest integer तक round करें।
A. 46
B. 47
C. 48
D. 49
सही उत्तर: C. 48
Tenths digit 6 है, इसलिए 47 को round-up करके 48 मिलेगा।
Practice MCQ
प्रश्न 2. 6,847 को nearest hundred तक round करें।
A. 6,700
B. 6,800
C. 6,900
D. 7,000
सही उत्तर: B. 6,800
Tens digit 4 है, इसलिए hundreds digit unchanged रहेगा। Answer=6,800।
Practice MCQ
प्रश्न 3. 12.746 को two decimal places तक round करें।
A. 12.74
B. 12.75
C. 12.76
D. 12.70
सही उत्तर: B. 12.75
Third decimal digit 6 है, इसलिए second decimal digit 4 से5 हो जाएगा। Answer=12.75।
Practice MCQ
प्रश्न 4. 0.007846 को three significant figures तक round करें।
A. 0.00784
B. 0.00785
C. 0.00780
D. 0.00800
सही उत्तर: B. 0.00785
First three significant digits 7, 8 और4 हैं। Next digit 6 होने से 4 बढ़कर5 होगा। Answer=0.00785।
Practice MCQ
प्रश्न 5. 398.6 + 201.3 का approximate value ज्ञात करें।
A. 500
B. 550
C. 600
D. 650
सही उत्तर: C. 600
398.6≈400 तथा201.3≈200। इसलिए approximate sum=600।
Practice MCQ
प्रश्न 6. 49.8 × 20.2 का approximate value ज्ञात करें।
A. 500
B. 800
C. 1000
D. 1200
सही उत्तर: C. 1000
49.8≈50 और20.2≈20। इसलिए 50×20=1000।
Practice MCQ
प्रश्न 7. 598 ÷ 29.9 का approximate value ज्ञात करें।
A. 10
B. 20
C. 30
D. 40
सही उत्तर: B. 20
598≈600 तथा29.9≈30। इसलिए 600÷30=20।
Practice MCQ
प्रश्न 8. −7.46 को one decimal place तक round करें।
A. −7.4
B. −7.5
C. −8.0
D. −7.0
सही उत्तर: B. −7.5
Hundredths digit 6 है, इसलिए tenths digit बढ़ेगा। अतः −7.46 → −7.5।
Practice MCQ
प्रश्न 9. 24.6% of 399.8 का approximate value ज्ञात करें।
A. 80
B. 90
C. 100
D. 120
सही उत्तर: C. 100
24.6%≈25% तथा399.8≈400। इसलिए 25% of400=100।
Practice MCQ
प्रश्न 10. 999.4 + 502.6 − 201.9 का approximate value ज्ञात करें।
A. 1200
B. 1250
C. 1300
D. 1400
सही उत्तर: C. 1300
999.4≈999, 502.6≈503 तथा201.9≈202। इसलिए 999+503−202=1300।