1 Reviewing number concepts To round to 3 significant figures, find the third significant digit and look at the value of the digit to the right of it. If it is 5 or greater, add one to the third significant digit and lose all of the other digits to the right. If it is less than 5, leave the third significant digit unchanged and lose all the other digits to the right as before. To round to a different number of significant figures, use the same method but find the appropriate significant digit to start with: the fourth for 4sf, the seventh for 7sf etc. If you are rounding to a whole number, write the appropriate number of zeros after the last significant digit as place holders to keep the number the same size.
The first significant digit of a number is the first non-zero digit, when reading from left to right. The next digit is the second significant digit, the next the third significant and so on. All zeros after the first significant digit are considered significant.
Worked example 14 Round: (a) 1.076 to 3 significant figures (a)
(b)
(b) 0.00736 to 1 significant figure
1.076
The third significant figure is the 7. The next digit is 6, so round 7 up to get 8.
= 1.08 (3sf)
Correct to 3 significant figures.
0.00736
The first significant figure is the 7. The next digit is 3, so 7 will not change.
= 0.007 (1sf)
Correct to 1 significant figure.
Exercise 1.17 Remember, the first significant digit in a number is the first nonzero digit, reading from left to right. Once you have read past the first non-zero digit, all zeros then become significant.
FAST FORWARD
You will use rounding to a given number of decimal places and significant figures in almost all of your work this year. You will also apply these skills to estimate answers. This is dealt with in more detail in chapter 5.
1 Round each number to 2 decimal places. (a) 3.185 (b) 0.064 (c) 38.3456 (f) 0.0456 (g) 0.005 (h) 41.567 (k) 0.062 (l) 0.009 (m) 3.016
(d) 2.149 (i) 8.299 (n) 12.0164
(e) 0.999 (j) 0.4236 (o) 15.11579
2 Express each number correct to: (i) 4 significant figures (a) 4512 (e) 25.716 (i) 0.00998
(ii) 3 significant figures
(b) 12 305 (f) 0.000765 (j) 0.02814
(c) 65 238 (g) 1.0087 (k) 31.0077
(iii) 1 significant figure (d) 320.55 (h) 7.34876 (l) 0.0064735
3 Change 2 5 to a decimal using your calculator. Express the answer correct to: 9
(a) 3 decimal places (d) 3 significant figures
(b) 2 decimal places (e) 2 significant figures
(c) 1 decimal place (f) 1 significant figure
Unit 1: Number
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