Topic 4: Numerical Concepts 1 (Indices) – Sample Activity

Context
The Government of Uganda has prepared an annual budget for running various activities. One municipality was given UGX 456.8 trillion. It was later given UGX 36.4 billion in a supplementary budget. An ordinary Ugandan would like to make sense of the amount of money received in order to see value for money for the social services in the municipality.
Hint
Knowledge of place value of numbers and budgetary provisions.

Support Material

Numerical


Task
As an urban planner, prepare a talk for the residents of the municipality on the amount of money they received.


Topic Summary
In this topic, you have learnt that:

  • all non-zero digits are significant. 1.234 g has 4 significant figures
    1.2 g has 2 significant figures
  • zeroes between non-zero digits are significant.
    1002 kg has 4 significant figures
    3.07 ml has 3 significant figures
  • zeroes to the left of the first non-zero digits are not significant; such
    zeroes merely indicate the position of the decimal point.
    0.001°C has only 1 significant figure
    0.012 g has 2 significant figures
  • zeroes to the right of a decimal point in a number are significant.
    0.023 ml has 2 significant figures
    0.200 g has 3 significant figures
  • when a number ends in zeroes that are not to the right of a decimal
    point, the zeroes are not necessarily significant.
  • 190 miles maybe 2 or 3 significant figures.
  • 50,600 calories maybe 3, 4 or 5 significant figures.
  • rounding of a number is as follows.
    • For the number of decimal places stated, count that number of digits to the right of the decimal and underline it.
    • The next number to its right is called the ’rounder decider’.
    • If the ’rounder decider’ is 5 or more, then round the previous digit up by 1.
    • If the ’rounder decider’ is 4 or less, then keep the previous digit the same.
  • in standard form, numbers are written as a x 10″, where 1 sa < 10 and n is an integer.
  • an index, or a power, is the small floating number that goes next to a number or letter. The plural of index is indices.
  • indices show how many times a number or letter has been multiplied by itself.
  • to multiply together two identical values or variables (letters) that are presented in index form with the same base, add the powers.
  • to divide two identical values or variables (letters) with the same base that are presented in index form, subtract the powers.
  • to raise a value or variable (letter) presented in index form to another index, multiply the powers together. Example: (p)3 = p4x3 = p12.
  • any letter or number to the power of zero is equal to 1.
  • an example of a fractional index is g”. The denominator of the fraction is the root of the number or letter, and the numerator of the fraction

Extended Tasks
1. An isosceles triangular garden measures 48.8 metres, 48.8 metres and 36.4 metres. Find the perimeter of the triangular garden in metres, giving your answer to the nearest 100 metre. Write your answer in standard form.

  1. It is given that one quadrillion is 1015 while one billion is expressed as (1 x 10°) and one trillion is expressed as (1 x 1012). Write down (3 x 10°) x (48 x 10″) in
    (a) billions.
    (b) trillions.
  2. Calculate the area of a rectangular garden which measures (6.5 x 10′) metres by (3.5 x 103) metres, leaving your answer in standard form.
    Find the length of the side of a square whose area is (15.4 x 10″) square metres, giving your answer to 3 significant figures
Magembe Solomon and Ashaba Fredrick

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Magembe Solomon and Ashaba Fredrick

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