Rounding and Significant Figures Quiz

Decimal Places

• To round a number to a specific decimal place, examine the digit after the desired place.
• If the digit is less than 5, the preceding digit remains unchanged.
• Examples:
  • 5.2895 (3 dp) = 5.290
  • 211.001 (1 dp) = 211.0
  • 1204.7999 (2 dp) = 1204.80
  • 2103.8070 (4 dp) = 2103.8070
  • 9.99999 (4 dp) = 10.000

Significant Figures

• Rules for significant figures:
  • Non-zero digits are significant.
  • Zeros between non-zero digits are significant.
  • Leading zeros are not significant.
  • Trailing zeros for a whole number with a decimal point are significant.
• Examples:
  • 52859 (sf) = 5
  • 80901 (sf) = 5
  • 0.0040 (sf) = 2

Approximation

• Approximation is a close but not exact value.
• The answer should have the same number of decimal places as the original number.
• Example:
  • Approximate 124 to the nearest tens = 120

Standard Form

• Standard form (scientific notation) represents very large or small numbers.
• Format: A x 10^n
  • A is a number ≥ 1 and < 10.
  • n is the number of places the decimal point is moved.
    • Left movement = positive n
    • Right movement = negative n
• Example:
  • 0.00067 = 6.7 x 10^-4

Indices

• Key terms: - index/power/exponent. - base (Example 4^2, 4 is the base.)
• Laws of Indices:
  • Any base to the power of zero is 1 (e.g., x^0 = 1).
  • Any base to the power of one is itself (e.g., y^1 = y).
  • Multiplication: Add powers (e.g., x^4 x x^2 = x^6).
  • Division: Subtract powers (e.g., x^9/x^6 = x^3).
  • Negative powers: 1/(base^positive power) (e.g., x^-n = 1/x^n).
  • Powers of powers: Multiply powers (e.g., (a^m)^n = a^(mn)).
  • Fractional powers: Denominator is the root, numerator is the power (e.g., x^m/n = (n√x)^m).
  • Fractional base powers: Apply the power to both numerator and denominator (e.g., (a/b)^m = a^m/b^m).

Binomial Expansion

• Methods for expanding binomials:
  • Separation of first bracket (e.g., (x+3) (2x+4) )
  • Box method
  • FOIL method (First, Outer, Inner, Last)

Factorisation

• Factorisation by HCF (Highest Common Factor)
• Factorisation by Grouping (Used with four terms, where brackets are always the same)

Consumer Arithmetic

Simple Interest

• Simple interest is interest charged on a borrowed sum.
• Key terms: Principal (amount borrowed), Rate (interest percentage), Time (in years).
• Formula: Simple Interest (SI) = (Principal x Rate x Time)/100
• Formula: Amount Accruing = Simple Interest + Principal

Compound Interest

• Interest calculated on the principal and accumulated interest.
• Formula: Amount Accruing (A) = P(1+r/100)^t; where r is rate and t is time (in years).
• Formula: Compound Interest (CI) = Amount Accruing - Principal

Appreciation

• Increase in value of an item over time.
• Formula: Amount Accruing (A) = P(1+r/100)^t

Depreciation

• Reduction in value of an asset over time.
• Formula: Value after depreciation = P(1 - r/100)^t

Mortgage

• Formulas for mortgage calculations are provided.

Hire Purchase

• Formulas for hire purchase calculations are provided.