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nuMber AnD AlgebrA • real numbers reMeMber 1. To round a decimal: Look at the first digit past the number of decimal places required. (a) If this number is less than 5, write the number with the number of decimal places required. (b) If this number is 5 or more, add 1 to the last decimal place being kept. If you add 1 to the last decimal place and the number in this position is a 9, the result is 10. The 0 is put in the last required place and the 1 is added to the digit in the next place to the left. 2. Rounding an answer gives a useful approximation of the original decimal. Use the symbol ö instead of = to show that the answer is an approximation. 3. A finite decimal terminates after a particular number of decimal places. 4. An infinite recurring decimal is obtained when the decimal places in the answer keep repeating and the amount left over each time also keeps repeating. An approximate answer can be found by rounding so that the answer includes one complete cycle of the pattern. 5. An infinite recurring decimal can be written exactly by placing a dot above the first and last digits of the repeating part or by drawing a line above the repeating part. exerCise 6C inDiViDuAl pAThWAys eBoo k plus eBook Activity 6-C-1 Rounding and repeating decimals doc-1777 Activity 6-C-2 More rounding and repeating decimals doc-1778 Activity 6-C-3 Advanced rounding and repeating decimals doc-1779 rounding and repeating decimals FluenCy 1 We10 Round the following to 2 decimal places. a 0.3241 b 0.863 d 13.049 92 e 7.128 63 g 71.260 39 h 0.0092 j 19.6979 k 0.3957 c f i l 1.246 10 100.813 82 0.185 00 0.999 2 Round the following to 1 decimal place. a 0.410 b 0.87 d 25.25 e 300.06 g 99.91 h 8.88 j 0.8989 k 93.994 c f i l 9.27 12.82 17.610 27 0.959 027 3 We11 Round the following to the number of decimal places shown in the brackets. a 2.386 214 (2) b 14.034 59 (1) c 0.027 135 (2) d 0.876 4903 (4) e 64.295 18 (4) f 0.382 04 (3) g 96.28 049 (1) h 3.0409 (2) i 8.902 (2) j 47.879 69 (3) k 0.099 498 632 (2) l 0.486 2590 (2) 4 MC a 13.179 rounded to 2 decimal places is equal to: d 13.27 e 13.19 b 0.2465 rounded to 1 decimal place is equal to: a 0.3 b 0.25 c 1.2 a 13.17 b 13.20 c 13.18 d 0.2 e 0.5 c 1.7688 rounded to 3 decimal places is equal to: a 1.768 b 1.770 c 1.778 d 1.769 e 1.800 d 2.998 rounded to 1 decimal place is equal to: a 3.0 b 2.9 c 2.8 d 3.1 e 3.9 Chapter 6 Decimals 195 number AND algebra • real numbers 5 WE 12 Round the following to the nearest unit. a 10.7 b 8.2 c 3.6 e 112.1 f 21.76 g 42.0379 i 0.12 j 0.513 k 0.99 d 92.7 h 2137.50 l 40.987 6 Write the following infinite recurring decimals using one of the short forms. a 2.555 . . . b 0.666 . . . c 12.888 88 . . . d 49.111 11 . . . e 0.262 626 . . . f 0.414 141 . . . g 0.913 913 . . . h 8.641 864 18 . . . i 0.040 121 21 . . . j 133.946 2462 . . . k 1.833 333 . . . l 0.127 7777 . . . 7 Convert each of the following to a decimal. Continue dividing until a pattern emerges, then round the answer to the number of dec­imal places indicated in the brackets. a 1 6 d 2 15 g 5 12 8 MC a b 1 3 (2) e 2 11 (3) h 1 7 (2) c 1 9 (1) (2) f 4 9 (1) (6) i 7 15 (2) (1) 3 5 as a decimal is: A 0.3 B 0.6 C 0.2 b 1.8888 . . . . written as an exact answer is: A 1.8 B 1.888 C 1.88 D 0.9 E 0.5 D 1.9 E 1.889 c 12.412 412 . . . written as an exact answer is: . A 12.412 d B 12.412 . . C 12.412 412 D 12.412 E 12.412 C 0.4 D 0.428 517 4 E 2.3 3 7 as a decimal in exact form is: . . A 0.428 571 B 0.428 . 9 Find decimal equivalents for the following fractions. Give your answer in exact form as either a finite decimal or an infinite recur­ring decimal. a 1 2 b 1 3 c 1 4 d 1 5 e 1 9 10 Using the answers from question 5, find decimal equivalents for the following ­fractions. a 7 2 b 4 2 3 c 3 4 d 3 4 5 e 7 9 Understanding 11 Round the following to the nearest ten. a 13 b 76 e 262 f 175 i 10 024 j 209 718.5 c 47 g 306.2 k 18.6 d 138 h 1484 l 5.92 12 Round the following to the nearest hundred. a 320 b 190 e 125 f 6751 i 1724 j 1 462 836.5 c 894 g 875.2 k 71 d 138 h 9750.051 l 47 13 Round the following to the nearest thousand. a 3426 b 5890 e 28 000 f 9462 i 12 780 j 862 c 12 300 g 1098 k 129 980 d 18 640 h 496 830 l 49 899 14 WE13 In the supermarket Christine’s shopping bill came to $27.68. As there are no 1- or 2-cent pieces, this amount must be rounded to the nearest 5 cents. How much will Christine pay for her shopping? 196 Maths Quest 7 for the Australian Curriculum