Rounding and Significant Figures Quiz

Study Notes

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.

Description

Test your understanding of rounding numbers, significant figures, and approximation. This quiz will cover key concepts including how to determine the correct number of decimal places and the rules for identifying significant figures. Practice with real examples to enhance your numerical skills.