Civil Service Exam (Subprofessional) Numerical Ability — Decimals & Scientific NotationRevision Notes

Formulas

Exam Tips

• Always align decimal points vertically when performing addition or subtraction
• Add zeros to the right of decimal numbers to make calculations easier
• Double-check your decimal point placement in final answers
• Practice reading decimal numbers aloud to avoid confusion during exams

Key Points

• Decimals represent parts of a whole using the base-10 system
• Each position after the decimal point has a specific place value: tenths, hundredths, thousandths, etc.
• Decimals can be converted to fractions and percentages
• Proper alignment of decimal points is crucial for accurate calculations
• Reading decimals correctly: 176.304 is 'one hundred seventy-six and three hundred four thousandths'

Definitions

Section Title

Understanding Decimals

Common Mistakes

• Misaligning decimal points when adding or subtracting
• Incorrect reading of decimal numbers (e.g., reading 0.05 as 'five hundredths' instead of 'five thousandths')
• Forgetting to add zeros as placeholders when necessary
• Confusing decimal place values with whole number place values

Formulas

Exam Tips

• Show your work clearly when counting decimal places
• Use estimation to check if your decimal answers are reasonable
• Practice mental math with simple decimal operations
• Remember that multiplying by powers of 10 moves decimal points right, dividing moves them left

Key Points

• Addition and subtraction require proper decimal point alignment
• Multiplication involves counting total decimal places in factors
• Division may require moving decimal points to make divisors whole numbers
• Rounding decimals follows standard rounding rules
• Calculator-free methods are essential for exam success

Definitions

Section Title

Decimal Operations

Common Mistakes

• Not counting decimal places correctly in multiplication
• Forgetting to move decimal points the same number of places in division
• Rounding too early in multi-step calculations
• Misplacing decimal points when converting between operations

Formulas

Exam Tips

• Memorize common equivalents: 1/4 = 0.25 = 25%, 1/2 = 0.5 = 50%, 3/4 = 0.75 = 75%
• Use the triangle method to remember P = R × B relationships
• Look for key words: 'is' often indicates percentage, 'of' often indicates base
• Practice converting between all three forms quickly

Key Points

• All three forms represent parts of a whole and can be converted between each other
• Common fraction-decimal-percentage equivalents should be memorized
• Percentage problems involve finding percentage, base, or rate
• The triangle method (P = R × B) helps solve percentage problems
• Mixed numbers and improper fractions require conversion for calculations

Definitions

Section Title

Fractions, Decimals, and Percentages

Common Mistakes

• Forgetting to convert percentages to decimals before calculations
• Confusing which number is the base vs. the percentage
• Not converting mixed fractions to improper fractions before operations
• Mixing up the P-R-B triangle relationships

Formulas

Exam Tips

• Count decimal places carefully when converting
• Remember: large numbers have positive exponents, small numbers have negative
• Practice with both very large and very small numbers
• Check your work by converting back to standard form

Key Points

• Scientific notation expresses very large or very small numbers efficiently
• Format: a × 10^n where 1 ≤ a < 10 and n is an integer
• Positive exponents indicate large numbers, negative exponents indicate small numbers
• Moving decimal point right decreases exponent, moving left increases exponent
• Essential for scientific calculations and engineering applications

Definitions

Section Title

Scientific Notation

Common Mistakes

• Making the coefficient less than 1 or greater than or equal to 10
• Using incorrect signs for exponents (positive for large, negative for small)
• Miscounting decimal place movements
• Forgetting to adjust the exponent when changing the coefficient