Metric System Conversions



H.W. # 2 Earth ScienceMetric System - ConversionsChanging metric units is as simple as multiplying or dividing by 10 or 1000. The diagram below shows you how to convert one unit into another by a series of multiplication or division. Metric System ConversionsConvert the following metric to metric values. 7cm = _______mm3,450mm = ________cm3.45 = ______cm10,946m = _____km18,300cm = ____m75.3km = _____m63.9cm = _____mm4m = _____cm63km = _____m10.19km = _____mm7km = _____mm1,938km = _____cmScientific NotationThe mass of the Earth is 5,979,000,000,000,000,000,000,000,000 kilograms. The molecular diameter of ammonia is 0.0000000297 centimeters. Very large and very small numbers are prone to errors when writing these numbers or typing them. To prevent these types of errors, these numbers can be written in a form called scientific notation. This allows numbers to be written as the product of a power of 10 and a number greater than or equal to 1, but less than 10. The mass of the Earth in scientific notation is 5.979 x 1027 kg and the molecular diameter of ammonia is 2.97 x 10-8 cm. The simplest method for conversion of standard notation to scientific notation is move the decimal. For very large numbers, move the decimal to the left, until it is after the first numeral. Count the number of places the decimal has moved. This then becomes the exponent on the 10. EXAMPLE Write 4,567,000 using scientific notation. 4,567,000 becomes 4.567000 The decimal place has been moved 6 places to the left. 4,567,000 = 4.567 x 106 For very small numbers, move the decimal to the right, until it is after the first non-zero numeral. Count the number of places the decimal has moved. This becomes a negative exponent on the 10. EXAMPLE Write 0.00000005436 using scientific notation. 0.00000005436 becomes 00000005.436 The decimal place has been moved 8 places to the right. 0.00000005436 = 5.436 x 10-8 Question 1Write the following exponential expressions in expanded form:101 =102 =103 =104 =10?1 =10?2 =10?3 =10?4 =Question 2Evaluate the following arithmetic expressions, expressing the answers in expanded form:3.6 × 102 =1.53 × 10?4 =8.2 × 101 =6 × 10?3 =Comment on the effect multiplication by a power of ten has on how a number is written._______________________________________________________________________________________________________________________________________________________________________________________________________________________________________Question 3Express the following numbers in scientific notation:0.00045 =23, 000, 000 =700, 000, 000, 000 =0.00000000000000000001 =0.000098 = ................
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