Civil Service Exam (Subprofessional) Numerical Ability — Decimals & Scientific NotationExam Answer Templates

Marks

1

Topic

Scientific Notation

Difficulty

easy

Template Id

T1

Examiner Tip

Count decimal places moved to determine the exponent - moving left gives positive exponent, moving right gives negative

Model Answer

0.00356 = 3.56 × 10^(-3)

Question Type

very_short_answer

Answer Structure

• Write the number in a × 10^n format where 1 ≤ a < 10 [1 mark]

Scoring Breakdown

Common Mark Deductions

• Incorrect exponent sign
• Coefficient not between 1 and 10
• Missing multiplication sign

Key Phrases To Include

• × 10^
• coefficient between 1 and 10

Marks

2

Topic

Decimal Operations

Difficulty

easy

Template Id

T2

Examiner Tip

Always align decimal points and add trailing zeros to make all numbers have the same number of decimal places

Model Answer

3.450 0.678 +12.900 ------- 17.028

Question Type

short_answer

Answer Structure

• Align decimal points vertically [1 mark]
• Add correctly and show final answer [1 mark]

Scoring Breakdown

Common Mark Deductions

• Misaligned decimal points
• Calculation errors
• Not showing working

Key Phrases To Include

• align decimal points
• add zeros for equal decimal places

Marks

3

Topic

Scientific Notation Operations

Difficulty

medium

Template Id

T3

Examiner Tip

When squaring scientific notation, square the coefficient and double the exponent

Model Answer

Step 1: Convert to standard form 4.56 × 10^5 = 456,000 Step 2: Calculate the square (456,000)² = (4.56 × 10^5)² = (4.56)² × (10^5)² = 20.7936 × 10^10 = 2.07936 × 10^11

Question Type

short_answer

Answer Structure

• Convert scientific notation to standard form [1 mark]
• Set up the square calculation [1 mark]
• Calculate and express answer in proper scientific notation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Incorrect decimal place movement
• Wrong exponent calculation
• Coefficient not between 1 and 10

Key Phrases To Include

• standard form
• square both coefficient and power
• proper scientific notation

Marks

2

Topic

Decimal Division

Difficulty

medium

Template Id

T4

Examiner Tip

Make divisor a whole number by multiplying both dividend and divisor by the same power of 10

Model Answer

2.88 ÷ 0.036 = 2880 ÷ 36 (multiply both by 1000) = 80 Therefore, 2.88 ÷ 0.036 = 80

Question Type

short_answer

Answer Structure

• Convert division to whole numbers by multiplying both by appropriate power of 10 [1 mark]
• Perform division and state final answer [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not showing conversion step
• Calculation errors
• Incorrect decimal elimination

Key Phrases To Include

• multiply both by same power of 10
• eliminate decimals

Marks

5

Topic

Scientific Notation Word Problems

Difficulty

hard

Template Id

T5

Examiner Tip

Always start with given information and show each step clearly for maximum marks

Model Answer

Given: - Initial bacteria count = 2.5 × 10^4 - Doubling time = 3 hours - Total time = 12 hours Step 1: Find number of doubling periods Number of periods = 12 ÷ 3 = 4 periods Step 2: Calculate growth factor After 4 doubling periods, bacteria multiply by 2^4 = 16 Step 3: Calculate final bacteria count Final count = Initial count × Growth factor = 2.5 × 10^4 × 16 = 2.5 × 16 × 10^4 = 40 × 10^4 = 4.0 × 10^5 Therefore, after 12 hours, there will be 4.0 × 10^5 bacteria.

Question Type

long_answer

Answer Structure

• Write given information clearly [1 mark]
• Calculate number of doubling periods [1 mark]
• Determine growth factor (2^4 = 16) [1 mark]
• Calculate final bacteria count [1 mark]
• Express answer in proper scientific notation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not stating given information
• Incorrect period calculation
• Wrong final notation format
• Calculation errors

Key Phrases To Include

• given information
• doubling periods
• growth factor
• scientific notation

Marks

1

Topic

Decimal Rounding

Difficulty

easy

Template Id

T6

Examiner Tip

Look at the third decimal place - if 5 or more, round up

Model Answer

23.4567 rounded to 2 decimal places = 23.46

Question Type

very_short_answer

Answer Structure

• Apply rounding rule and give correct answer [1 mark]

Scoring Breakdown

Common Mark Deductions

• Incorrect rounding
• Wrong number of decimal places

Key Phrases To Include

• rounded to
• decimal places

Marks

2

Topic

Scientific Notation Multiplication

Difficulty

medium

Template Id

T7

Examiner Tip

When multiplying scientific notation, multiply coefficients and add exponents

Model Answer

(3.2 × 10^6) × (1.5 × 10^(-3)) = 3.2 × 1.5 × 10^6 × 10^(-3) = 4.8 × 10^(6-3) = 4.8 × 10^3

Question Type

short_answer

Answer Structure

• Multiply coefficients and add exponents [1 mark]
• Express answer in proper scientific notation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Subtracting instead of adding exponents
• Incorrect coefficient multiplication

Key Phrases To Include

• multiply coefficients
• add exponents

Marks

1

Topic

Scientific Notation

Difficulty

easy

Template Id

T8

Examiner Tip

Count how many places the decimal moves from its original position

Model Answer

456,000,000 = 4.56 × 10^8

Question Type

very_short_answer

Answer Structure

• Write in a × 10^n format where 1 ≤ a < 10 [1 mark]

Scoring Breakdown

Common Mark Deductions

• Wrong exponent
• Coefficient outside 1-10 range

Key Phrases To Include

• × 10^
• move decimal point

Marks

2

Topic

Decimal Operations

Difficulty

easy

Template Id

T9

Examiner Tip

Add zeros to make all numbers have the same decimal places for easier calculation

Model Answer

15.600 - 8.970 +3.045 ------ 9.675

Question Type

short_answer

Answer Structure

• Align decimal points and add trailing zeros [1 mark]
• Perform calculations correctly [1 mark]

Scoring Breakdown

Common Mark Deductions

• Misalignment
• Calculation errors
• Not showing working

Key Phrases To Include

• align decimal points
• trailing zeros

Marks

3

Topic

Scientific Notation Operations

Difficulty

medium

Template Id

T10

Examiner Tip

For reciprocal of scientific notation, find reciprocal of coefficient and change sign of exponent

Model Answer

Step 1: Convert to scientific notation 0.000034 = 3.4 × 10^(-5) Step 2: Find reciprocal Reciprocal = 1/(3.4 × 10^(-5)) = 1/3.4 × 1/10^(-5) = 0.294 × 10^5 = 2.94 × 10^4

Question Type

short_answer

Answer Structure

• Convert decimal to scientific notation [1 mark]
• Set up reciprocal calculation [1 mark]
• Calculate reciprocal and express in proper scientific notation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Incorrect initial conversion
• Wrong reciprocal calculation
• Improper final notation

Key Phrases To Include

• scientific notation
• reciprocal
• invert coefficient and exponent

Marks

3

Topic

Scientific Notation Applications

Difficulty

medium

Template Id

T11

Examiner Tip

Always start by clearly stating what is given and what needs to be found

Model Answer

Given: - 1 light-year = 9.46 × 10^12 km - Distance = 4.2 light-years Distance in km = 4.2 × 9.46 × 10^12 = 39.732 × 10^12 = 3.9732 × 10^13 km Therefore, the nearest star is 3.97 × 10^13 km away.

Question Type

short_answer

Answer Structure

• Write given information [1 mark]
• Set up multiplication correctly [1 mark]
• Calculate and express in proper scientific notation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not stating given information
• Calculation errors
• Incorrect final notation

Key Phrases To Include

• given
• light-year
• scientific notation

Marks

2

Topic

Scientific Notation Division

Difficulty

medium

Template Id

T12

Examiner Tip

When dividing scientific notation, divide coefficients and subtract exponents

Model Answer

(2.4 × 10^3) ÷ (6.0 × 10^(-2)) = (2.4 ÷ 6.0) × 10^(3-(-2)) = 0.4 × 10^5 = 4.0 × 10^4

Question Type

short_answer

Answer Structure

• Divide coefficients and subtract exponents [1 mark]
• Express final answer in proper scientific notation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Adding instead of subtracting exponents
• Incorrect coefficient division

Key Phrases To Include

• divide coefficients
• subtract exponents

Marks

3

Topic

Decimal Applications

Difficulty

medium

Template Id

T13

Examiner Tip

Always state the formulas before substituting values

Model Answer

Given: Length = 45.6 m Width = 23.75 m Area = Length × Width = 45.6 × 23.75 = 1083.0 m² Perimeter = 2(Length + Width) = 2(45.6 + 23.75) = 2(69.35) = 138.7 m

Question Type

short_answer

Answer Structure

• Write given information and formulas [1 mark]
• Calculate area correctly [1 mark]
• Calculate perimeter correctly [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not stating formulas
• Calculation errors
• Missing units

Key Phrases To Include

• given
• area formula
• perimeter formula

Marks

2

Topic

Decimal Comparison

Difficulty

easy

Template Id

T14

Examiner Tip

Add trailing zeros to compare decimals with different decimal places

Model Answer

Comparing the decimals: 3.45 = 3.450 3.405 < 3.45 = 3.450 < 3.54 Ascending order: 3.405, 3.45, 3.450, 3.54 Note: 3.45 = 3.450

Question Type

short_answer

Answer Structure

• Compare decimals by examining each decimal place [1 mark]
• Arrange in correct ascending order [1 mark]

Scoring Breakdown

Common Mark Deductions

• Incorrect comparison
• Wrong ordering

Key Phrases To Include

• compare
• ascending order
• decimal places

Marks

5

Topic

Scientific Notation in Chemistry

Difficulty

hard

Template Id

T15

Examiner Tip

This is a classic chemistry application - always relate to real-world significance like atomic mass

Model Answer

Given: - Mass of one hydrogen atom = 1.67 × 10^(-27) kg - Number of atoms = 6.02 × 10^23 (Avogadro's number) To find: Total mass of 6.02 × 10^23 hydrogen atoms Solution: Total mass = Number of atoms × Mass per atom = (6.02 × 10^23) × (1.67 × 10^(-27)) = 6.02 × 1.67 × 10^23 × 10^(-27) = 10.0534 × 10^(23-27) = 10.0534 × 10^(-4) = 1.00534 × 10^(-3) kg ≈ 1.01 × 10^(-3) kg Therefore, the mass of 6.02 × 10^23 hydrogen atoms is approximately 1.01 × 10^(-3) kg or 1.01 g.

Question Type

long_answer

Answer Structure

• Write given information clearly [1 mark]
• State what needs to be found [1 mark]
• Set up the multiplication correctly [1 mark]
• Perform calculation with proper exponent handling [1 mark]
• Express final answer in proper scientific notation with appropriate rounding [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not stating given data
• Incorrect exponent calculation
• Wrong final notation
• No rounding indication

Key Phrases To Include

• given
• to find
• Avogadro's number
• scientific notation
• mass calculation