This document discusses estimation and approximation using significant figures. It provides examples of rounding numbers to 1 and 2 significant figures. Key points covered include: - Using estimation to check answers and writing numbers to significant figures. - The definition of significant figures and how to identify them in a number. - Methods for rounding numbers to 1 and 2 significant figures by ignoring leading zeros and rounding based on the digit in the next place value. - Examples of estimating calculations by rounding numbers to 1 significant figure before calculating.

3. Write approximations for these numbers 18.9 10.2 102.4 172 1005 1779.3 0.45

4. Significant figures The first significant figure of a number is the first non-zero number from the left. Here the 5 is the first significant figure 0.054 1054 And here the 1 is the first significant figure Zeros are only non-significant if they are sandwiched between tow other numbers

5. 0.074 0.074 Find the first significant figure (7) Look a the next number 4 – if it is 5 or more increase the 7, if it is less than five leave the 7 alone 0.07 So 0.074 to 1 sig fig is 0.07

6. 704 704 Find the first significant figure (7) Look a the next number 0 – if it is 5 or more increase the 7, if it is less than five leave the 7 alone. It’s not a decimal so all the other digits need to be zeros to keep the place value 700 So 704 to 1 sig fig is 700

7. 0.076 0.076 Find the first significant figure (7) Look a the next number 6 – if it is 5 or more increase the 7, if it is less than five leave the 7 alone 0.08 So 0.076 to 1 sig fig is 0.08

8. 751 751 Find the first significant figure (7) Look a the next number 5 – if it is 5 or more increase the 7, if it is less than five leave the 7 alone. 800 So 751 to 1 sig fig is 800

9. Write these numbers to 1 significant figure 18.9 20 10.2 10 102.4 100 172 200 1005 1000 2000 1779.3 0.5 0.45

11. Find the second significant figure from the left

12. If the number to the right is 5 or more, increase the second number by 1

15. Turn all the remaining digits to zero Answer 2684 to 2 significant figures is 2700.

16. Another way of looking at it is to decide if 2684 is nearer to 2700or 2600 2684 2600 2700 2650

17. Writing numbers to 1 significant figure can help with checking answers and with estimating For example Calculate: 48 x 102 52.4 Using a calculator: 4896 = 93.43511…. 52.4 Estimating – using 1 sig. fig.: 48 x 102 = 52.4 50 x 100 = 50 100 Check

18. Writing numbers to 1 significant figure can help with checking answers and with estimating For example Calculate: 5.4x 19 2.4 Using a calculator: 102.6 = 42.75 2.4 Estimating – using 1 sig. fig.: 10 5 x 20= 2 50 Check

19. Now try these Estimate: 140 x 19 2.1 Estimate: 540x 1.92 3.9 Estimate: 1040x 192 48

22. The 4 to the left becomes as zero

23. So write 0.00854.Answer 0.00854 to 2 significant figures is 0.0085