S1G3 Math CH3 Notes (NBSS)

NAVAL BASE SECONDARY SCHOOL MATHEMATICS DEPARTMENT Sec 1 Express Mathematics Chapter 3 : Approximation and Estimation Notes Name: ________________________________ ( ) Class: _________ Date: ____________ 1 3.1 Introduction to Approximation Objectives: At the end of the lessons, students should be able to ● round off numbers to a required number of decimal places ● round off numbers to a required number of significant figures Approximation is the rounding of numbers to a required degree of accuracy. Prerequisite Let’s recap on the number placing positions. Fill in the blanks with a number from the following figure. 1894.237 (i) Thousands place: ______ (v) Thousandths place: ______ (ii) Hundreds place: ______ (vi) Hundredths place: ______ (iii) Tens place: ______ (vii) Tenths place: ______ (iv) Ones place: ______

2 Example 1 (Rounding off) Based on the following number, correct to: 16.49583 (a) the nearest whole number. Ans: 16 (b) two decimal places. Ans: 16.50 (c) the nearest integer Ans: 16 Practice 1 Round off the following correct to (i) two decimal places and (ii) the nearest whole number: (a) $12.3125 (b) 57.6283 (c) 1.99976 cm (d) 101.3333 kg (e) 3.23495 (f) $ 4.5671 When rounding off numbers: (1) Round down if the digit under consideration is 4 or less. Round up if the digit under consideration is 5 or more. (2) Check the value of approximation against the original value

3 Example 2 (Significant figures) Let us consider the following case. A grain of table salt weighs 0.0001208g. If the answer is rounded off to 3 decimal places, the weight of the salt is now: 0.0001208 g = 0.000 g (3 d.p.) This value we obtain is not useful for calculations! Instead of rounding off to 3 decimal places, we round off according to significant figures. 5 Rules for Determining Number of Significant Figures: All non-zero digits are significant. E.g. 34.58 has 4 significant figures. All zeros between non-zero digits are significant. E.g. 10237 has 5 significant figures. In a decimal, all zeros after decimal points and a non-zero number are significant. E.g. 1.7890 has 5 significant figures. In a decimal, all zeros after a non-zero digit are significant. E.g. 0.0056 has 2 significant figures. All zeros at the end of a whole number may or may not be significant depending on how the number is rounded off E.g. 10010 has 4 significant figures OR 5 significant figures.

4 Practice 2 Based on the following number, correct to: 21.03460970 (a) 2 significant figures. Ans: ___________ (b) 3 significant figures. Ans: ___________ (c) 4 significant figures. Ans: ___________ (d) 5 significant figures. Ans: ___________ (e) 7 significant