ROUNDING APPROXIMATIONS LESSON 3 ROUNDING NUMBERS SIGNIFICANT FIGURES

ROUNDING & APPROXIMATIONS: LESSON 3 ROUNDING NUMBERS (SIGNIFICANT FIGURES)

SIGNIFICANT FIGURES 2 6 9 3 1 st 2 nd 3 rd 4 th Significan t Figure

ROUND TO THE 3 RD SIGNIFICANT FIGURE 1 2 7 6 3 1 1 st 2 nd 3 rd 4 th 5 th 6 th Significan t Figure Significan t Figure

ROUNDING TO THE NEAREST 1000 127631 Rounded (Less Precise) 1 st 2 nd s. f. 3 rd s. f. 4 th s. f. 5 th 6 th s. f. 000

ROUNDING TO THE NEAREST 1000 12 7631 Rounded (Less Precise) 1 st 2 nd s. f. 3 rd s. f. 4 th s. f. 5 th 6 th s. f. 000

ROUNDING TO THE NEAREST 1000 127631 Rounded (Less Precise) 1 st 2 nd s. f. 3 rd s. f. 4 th 5 th s. f. 6 th s. f. 12? 000 keep zero

1 2 77 6 3 1 +1 1 2? 0 0 0 same

1 2 77 6 3 1 +1 1 2 000 same

127631 +1 1 27000 same ROUND DOWN

1 27 6 3 1 +1 same 8 1 2? 0 0 0 7 ROUND DOWN

1 27 6 3 1 +1 same 8 ROUND UP 1 2? 0 0 0 7 ROUND DOWN

1 27 6 3 1 +1 same 8 1 2? 0 0 0 7 Smaller than 5 (0, 1, 2, 3, 4)

1 27 6 3 1 +1 same 8 1 2? 0 0 0 7 Smaller than 5 (0, 1, 2, 3, 4)

1 27 6 3 1 +1 same 5 or Greater (5, 6, 7, 8, 9) 8 1 2? 0 0 0 7 Smaller than 5 (0, 1, 2, 3, 4)

1 27 6 3 1 +1 8 5 or Greater (5, 6, 7, 8, 9) 1 2? 0 0 0

1 27 6 3 1 Rounded to 3 significant figures (3 s. f) 1 28000

WHY ROUND NUMBERS? - For Approximation / Estimation /Quick Calculation we round to the 1 st significant figure 27. 12 x 3. 96 Is approximately 30 x 4 - Don’t need very much Precision We can say Malta has a population of around 500, 000 (rounded to 1 s. f. ), rather than saying a population of 514, 564 (which changes every second!)

ROUND TO THE 1 ST SIGNIFICANT FIGURE 2 6 9 3 Rounded to the 1 st Significant Figure 1 st 2 nd 3 rd 4 th Significan t Figure 3 0 0 0

ROUND TO THE 1 ST SIGNIFICANT FIGURE 3 4 1 st s. f. Rounded to the 1 st Significant Figure 2 nd s. f. 3 0 7 1 3 rd s. f. 0 4 th s. f. 0 = 30

ROUND TO THE 1 ST SIGNIFICANT FIGURE 0 NOT Significant 2 5 3 1 st Significan t Figure 2 nd s. f. 3 rd s. f. Which is the 1 st significant figure? The first non-zero digit (reading from left to right)

ROUND TO THE 1 ST SIGNIFICANT FIGURE 0 2 5 3 1 st s. f. Rounded to the 1 st Significant Figure 0 2 nd s. f. 3 rd s. f. 3 0 0 = 0. 3

ROUND TO THE 2 ND SIGNIFICANT FIGURE 0 0 0 6 1 9 Which is the 1 st significant figure? The first non-zero digit (reading from left to right)

ROUND TO THE 2 ND SIGNIFICANT FIGURE 0 NOT Significant 0 0 6 1 9 NOT Significant 1 st Significan t Figure 2 nd s. f. Which is the 1 st significant figure? The first non-zero digit (reading from left to right) 3 rd s. f.

ROUND TO THE 2 ND SIGNIFICANT FIGURE 0 0 0 6 1 9 1 st s. f. Rounded to the 2 nd Significant Figure 0 2 nd s. f. 3 rd s. f. 0 0 6 2 0 =0. 0062 keep same or +1 zero

ROUND TO THE 3 RD SIGNIFICANT FIGURE 7 0 0 8 0 9 1 st s. f. 2 nd s. f. 3 rd s. f. 4 th s. f. 5 th s. f. Which is the 3 rd significant figure? Any zeros between two significant digits are significant 6 th s. f.

ROUND TO THE 3 RD SIGNIFICANT FIGURE 7 0 0 8 0 9 1 st s. f. 2 nd s. f. 3 rd s. f. 4 th s. f. 5 th s. f. 6 th s. f. 7 0 1 0 0 0

ROUND TO THE 3 RD SIGNIFICANT FIGURE 7 0 0 8 0 9 H Th Th 7 0 1 H T U

ROUND TO THE 3 RD SIGNIFICANT FIGURE 7 0 0 8 0 9 H Th Th H T U 7 0 1 0 0 0 H Th Th H T U

CONCLUSION - The first significant figure is the first non-zero digit (reading from left to right) - Any zeros between two significant digits are significant 0 6 0 3 NOT Significant 1 st 2 nd 3 rd Significan t Figure