Section one - Numbers Part 2

Section one - Numbers Part 2

1. Rounding Numbers

   • Decimal Places (d.p.)
     • Identify the position of the 'Last Digit' from the number of decimal places
       • Look at the next digit to the right
         • If it is 5 or more, round up
         • If it is 4 or less, round down
         • There must be no more digits after the last digits
   • Significant Figures
     • The 1st significant figure of any number is the first digit which isn't a zero
       • The 2nd, 3rd, 4th etc significant figures follow on immediately after the 1st, whether they're zeros
         • After rounding the last digit, end zeros must be filled in up to, but not beyond, the decimal point
           • No extra zeros must be put after the decimal point

2. Estimating

   • Estimating Calculations
     • Round all the numbers to the Easiest ones
       • 127.8 + 41.9 = 130 + 40 = 170
       • 56.5 x 3.2 = 60 x 3 = 180
   • Estimating Square Roots
     • Find two square numbers, one either side of the number you're given
       • Decide which number it's closest to, and make an estimate of the digit after the decimal point
     • √87 to 1d.p.
       • √81 = 9 or √100 = 10
         • √81 is closer
           • √87 = 9.3

3. Bounds

   • Upper and Lower Bounds
     • 2.4 kg to the nearest 0.1 kg
       • lower bound = 2.4 - 0.05 = 2.35 kg
       • Upper Bound = 2.4 + 0.05 = 2.45 kg
       • 2.35 kg < m < 2.45 kg
   • When a measurement is rounded to a given unit, the actual measurement can be anything up to half a unit bigger or smaller
   • Truncation
     • When a measurement is truncated to a given unit, the actual measurement can be up to a whole unit bigger but no smaller

4. Standard form

   • Multiplying and Dividing
     • rearrange to put the front numbers and the power of 10 together
       • Multiply or divide the front numbers and use the power rules to multiply or divide the powers of 10
         • Make sure your answer is still in Standard Form
   • Rules
     • A x 10n
     • The front number must always be between 1 and 10
       • The power of 10, n, is how far the decimal point moves
         • n is positive for big numbers, n is negative for small numbers
   • Adding and Subtracting
     • Make sure the powers of 10 are the same
       • Add or subtract the front numbers
         • Convert the answer to Standard Form