Decimal Fractions

Operations with decimals and fractions

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Decimal fractions represent parts of a whole using base-10 notation, where each digit after the decimal point represents tenths, hundredths, thousandths, etc. Understanding decimal operations, conversions between fractions and decimals, and recurring decimals is essential for solving quantitative aptitude problems efficiently.

Key formulas and rules

Decimal to Fraction: Write the decimal as numerator without decimal point, denominator as 1 followed by zeros equal to decimal places. Example: 0.75 = 75/100 = 3/4

Fraction to Decimal: Divide numerator by denominator. Example: 3/4 = 0.75

Terminating Decimal: A fraction p/q in lowest terms has terminating decimal expansion iff prime factors of q are only 2 and/or 5

Recurring Decimal: 0.a b = (ab)/99, 0.a bc = (abc)/999, 0.0a b = (ab)/990

Pure Recurring: All digits repeat (e.g., 0.333... = 1/3). Mixed Recurring: Some digits don't repeat (e.g., 0.1666... = 1/6)

Comparing Decimals: Compare digit by digit from left to right after equalizing decimal places

Decimal Addition/Subtraction: Align decimal points vertically, then perform operation

Decimal Multiplication: Multiply as whole numbers, then place decimal point counting total decimal places in factors

Decimal Division: Shift decimal points to make divisor whole number, then divide

Key concepts

Types of Decimals

Terminating decimals end after finite digits (e.g., 0.5, 0.25). Non-terminating decimals continue infinitely: pure recurring where all digits repeat (0.333...), and mixed recurring where some digits don't repeat (0.1666...). A fraction gives terminating decimal only when denominator (in lowest terms) has prime factors 2 and/or 5 only.

Decimal Fractions

Key formulas and rules

Key concepts

Types of Decimals

Converting Recurring Decimals to Fractions

Decimal Operations

Comparing and Ordering Decimals

Rounding and Approximation

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Key formulas and rules

Key concepts

Types of Decimals

Converting Recurring Decimals to Fractions

Decimal Operations

Comparing and Ordering Decimals

Rounding and Approximation

Worked examples

Example 1

Example 2

Example 3

Example 4

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

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