Find the value of $ 0.3\bar{6} + 0.7\bar{23}$. | Mathematics MCQ | Examoogle

Back to Practice Questions

MathematicsPrevious Year Paper 2024

Prev Next

Find the value of $0.3\overline{6} + 0.7\overline{23}$ .

$1\frac{41}{495}$

$1\frac{89}{990}$

$1\frac{26}{33}$

$1\frac{31}{330}$

Correct Answer

📐 MA • Math Fraction ConversionMathematicsPrevious Year Paper 2024

Option B

$1\frac{89}{990}$

Quick Summary:

Convert both to fractions with a common denominator of 990: $0.3666... = 363/990$ and $0.72323... = 716/990$ .

🎯

Crack Previous Year Paper 2024 with Examoogle SuperTeachers

Get Free Demo Classes & Live Mocks →

📐MAMath SolutionFraction Conversion

📋 Given

Two repeating decimals: 0.36 (with 6 repeating) and 0.723 (with 23 repeating).

🔢 Formula Used

0.a‾=a9,0.ab‾=ab−a90,0.abc‾=abc−a9900.\overline{a} = \frac{a}{9}, \quad 0.a\overline{b} = \frac{ab-a}{90}, \quad 0.a\overline{bc} = \frac{abc-a}{990}0.a=9a​,0.ab=90ab−a​,0.abc=990abc−a​

⚡ Exam Hall Shortcut / Speed Trick

Convert both to fractions with a common denominator of 990: $0.3666... = 363/990$ and $0.72323... = 716/990$ .

⚠️ Common Student Trap / Pitfall

Students often treat $0.3\overline{6}$ as $36/99$ instead of $33/90$ or $11/30$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Convert 0.36 (6 repeating) to fraction

Let $x = 0.3666...$ . Then $10x = 3.666...$ and $100x = 36.666...$ . Thus $90x = 36.666... - 3.666... = 33$ . So $x = 33/90 = 11/30$ .

0.36‾=36−390=3390=11300.3\overline{6} = \frac{36-3}{90} = \frac{33}{90} = \frac{11}{30}0.36=9036−3​=9033​=3011​

Convert 0.723 (23 repeating) to fraction

The value $0.7\overline{23}$ can be written as $7/10 + 23/990$ . Combining these gives $(693 + 23)/990 = 716/990$ .

0.723‾=723−7990=7169900.7\overline{23} = \frac{723-7}{990} = \frac{716}{990}0.723=990723−7​=990716​

Add the two fractions

Convert $11/30$ to a denominator of 990 by multiplying numerator and denominator by 33: $(11 \times 33) / (30 \times 33) = 363/990$ . Now add: $(363 + 716) / 990 = 1079/990$ .

363990+716990=1079990=189990\frac{363}{990} + \frac{716}{990} = \frac{1079}{990} = 1\frac{89}{990}990363​+990716​=9901079​=199089​

✅

B is correct because the sum of the converted fractions $363/990 + 716/990$ equals $1079/990$ , which simplifies to $1\frac{89}{990}$ .

Core Concepts Used

Click any tag to open in AI Tutor

Recurring Decimals Fraction Arithmetic Denominator Normalization

💡 EXAM TIP

This concept is fundamental for simplifying complex algebraic expressions involving periodic decimals often found in RRB and SSC examinations.

Was this solution helpful?

⚡ Practice on Android App · 4.8 ★

Solve 10,000+ More Questions with AI Tutor

Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.

Free Download • 100K+ Aspirants

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)