Scientific Notation, Engineering Notation
Scientific Notation, Engineering Notation Scientific Notation, Engineering Notation
Reasons for using Scientific Notation.1. Very large and very small numbers can be expressed in a simple,compact form.Consider these two examples.The mass of the moon is:73 600 000 000 000 000 000 000 kg. = 7.36 × 10 22 kg.The charge on one electron is:0.000 000 000 000 000 000 160 2 C = 1.602 × 10 -19 CThe size of the number is more easily seen when written in scientificnotation.Errors are less likely when writing the number, if the number is inscientific form.2. The number of significant figures can be easily determined. It is easyto see that4.545 × 10 6 has four significant figures.3. Calculations can be simplified by using index laws. For example:350000 × 102000000 = 3.5 × 10 5 × 1.02 × 10 8=3.5 × 1.02 × 10 5 +8= 3.57 × 10 13Exercise 1Write the following numbers in Scientific Notation.(a) 58000 (b) 0.0026(c) 70.6 (d) 0.3(e) 2 400 000 (f) 0.000 000 684(g) 0.0704 (h) 0.260Exercise 2Write the following numbers in decimal form.(a) 7 × 10 2 (b) 4 × 10 0(c) 3.459× 10 3(d) 5.96 × 10 −5Answers1. (a) 5.8× 10 (b) 2.6× 10 (c) 7.06× 10 (d) 3× 10 (e) 2.4× 10 (f) 6.84× 10 (g) 7.04×104 −3 −1 6 −7 −2−1(h) 2.60×102. (a) 700 (b) 4 (c) 3459 (d) 0.0000596Page 2 of 7
EngineeringNotation“Engineering Notation” is similar to scientific notation. In engineeringnotation the powers of ten are multiples of 3.A number written in Engineering Notation is written in the form:a = b x 10 n• b is a number from 1 to less than 1000• n is a multiple of threeTo write a number in engineering notation:• shift the decimal point in “groups” of three places to give anumber between 1 and 1000• multiply by a power of 10 equal to the number of places thedecimal point has been moved.The power of 10 is positive if the decimal point is moved to the leftand negative if the decimal point is moved to the right.Examples1. Write 1635 000 000 in engineering notation.1635 000 000 = 1.635×109Move the decimal point three groups of three places ( 9 places) tothe left. The number is now between 1 and 1000 and the power of 10is 9.2. Write 0.4 in engineering notation.−0. 4 = 400 × 10 3Move the decimal point one group of three places (3 places) toright. In this case we have to add zeros for the last two places. Thenumber is now between 1 and 1000. The power of 10 is −3.3. Write 0.000 0045 in engineering notation.0.000 0045 = 4.5×10 −6Move the decimal point two groups of three places ( 6 places) to theright. The number is now between 1 and 1000 and the power of 10 is− 6.Page 3 of 7
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- Page 7: Answers3. ( a) 53.8× 10 (b) 145×
<strong>Engineering</strong><strong>Notation</strong>“<strong>Engineering</strong> <strong>Notation</strong>” is similar to scientific notation. In engineeringnotation the powers of ten are multiples of 3.A number written in <strong>Engineering</strong> <strong>Notation</strong> is written in the form:a = b x 10 n• b is a number from 1 to less than 1000• n is a multiple of threeTo write a number in engineering notation:• shift the decimal point in “groups” of three places to give anumber between 1 and 1000• multiply by a power of 10 equal to the number of places thedecimal point has been moved.The power of 10 is positive if the decimal point is moved to the leftand negative if the decimal point is moved to the right.Examples1. Write 1635 000 000 in engineering notation.1635 000 000 = 1.635×109Move the decimal point three groups of three places ( 9 places) tothe left. The number is now between 1 and 1000 and the power of 10is 9.2. Write 0.4 in engineering notation.−0. 4 = 400 × 10 3Move the decimal point one group of three places (3 places) toright. In this case we have to add zeros for the last two places. Thenumber is now between 1 and 1000. The power of 10 is −3.3. Write 0.000 0045 in engineering notation.0.000 0045 = 4.5×10 −6Move the decimal point two groups of three places ( 6 places) to theright. The number is now between 1 and 1000 and the power of 10 is− 6.Page 3 of 7
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