Why write numbers in scientific notation Understanding physics will help you describe in great detail how the world works. However, the characteristics of the world span an enormous range of numbers. The mass of an electron is 0.000000000000000000000000000000911 kg (incredibly tiny!). The mass of the Sun is 1,989,000,000,000,000,000,000,000,000,000 kg (incredibly massive!). If you had to write, interpret, or use these numbers as written, you could very easily end up making a minor math error. Scientific notation was invented to easily express numbers that are too large or too small to be conveniently written in decimal form. The advantages of scientific notation are it 1) is compact, 2) helps articulate significant figures, and 3) works with numbers of any size. The traditional format for numbers written in scientific notation is m × 10 n is where m is a number between 1 and 10 and n is an integer (either positive or negative). For the examples above, the mass of an electron can be written as 9.11 × 10-31 kg and the mass of the Sun can be written as 1.989 × 1030 kg . Converting decimals to scientific notation A day has 86,400 second (s) . Notice that the decimal point is to the far right of the number. The first part of scientific notation is a number between 1 and 10. Move the decimal point to the left to obtain 8.64, which equals m in our traditional notation. The value for n is given by the number of places the decimal point was moved from its location in 86,400 to 8.64. Thus, 86,400 s = 8.64 × 104 s . Because the decimal was moved four places to the left (and the value is larger than 1), the exponent is a positive integer. If you had a very precise clock, you could write this as 8.640 × 104 s , or 8.6400 × 104 s . The number of digits you keep in the first part of the notation describes the precision of your value and determines the number of significant digits. As another example, the fastest glacier in the world has an average speed of 0.0012 mile/hour. The first part of scientific notation is a number between 1 and 10. Move the decimal point to the right to obtain 1.2, which equals m in our traditional notation. The value for n is given by the number of places the decimal point was moved from its location in 0.0012 to 1.2. Thus, 0.0012 mile/hour = 1.2 × 10-3 mile/hour. Because the decimal was moved three places to the right, and the value is smaller than 1, the exponent is a negative integer. Part A - Write this large number in scientific notation. Determine the values of m and n when the following mass of the Earth is written in scientific notation: 5,970,000,000,000,000,000,000,000 kg . Enter m and n , separated by commas.

Why write numbers in scientific notation Understanding physics will help you describe in great detail how the world works. However, the characteristics of the world span an enormous range of numbers. The mass of an electron is 0.000000000000000000000000000000911 kg (incredibly tiny!). The mass of the Sun is 1,989,000,000,000,000,000,000,000,000,000 kg (incredibly massive!). If you had to write, interpret, or use these numbers as written, you could very easily end up making a minor math error. Scientific notation was invented to easily express numbers that are too large or too small to be conveniently written in decimal form. The advantages of scientific notation are it 1) is compact, 2) helps articulate significant figures, and 3) works with numbers of any size. The traditional format for numbers written in scientific notation is m × 10 n is where m is a number between 1 and 10 and n is an integer (either positive or negative). For the examples above, the mass of an electron can be written as 9.11 × 10-31 kg and the mass of the Sun can be written as 1.989 × 1030 kg . Converting decimals to scientific notation A day has 86,400 second (s) . Notice that the decimal point is to the far right of the number. The first part of scientific notation is a number between 1 and 10. Move the decimal point to the left to obtain 8.64, which equals m in our traditional notation. The value for n is given by the number of places the decimal point was moved from its location in 86,400 to 8.64. Thus, 86,400 s = 8.64 × 104 s . Because the decimal was moved four places to the left (and the value is larger than 1), the exponent is a positive integer. If you had a very precise clock, you could write this as 8.640 × 104 s , or 8.6400 × 104 s . The number of digits you keep in the first part of the notation describes the precision of your value and determines the number of significant digits. As another example, the fastest glacier in the world has an average speed of 0.0012 mile/hour. The first part of scientific notation is a number between 1 and 10. Move the decimal point to the right to obtain 1.2, which equals m in our traditional notation. The value for n is given by the number of places the decimal point was moved from its location in 0.0012 to 1.2. Thus, 0.0012 mile/hour = 1.2 × 10-3 mile/hour. Because the decimal was moved three places to the right, and the value is smaller than 1, the exponent is a negative integer. Part A - Write this large number in scientific notation. Determine the values of m and n when the following mass of the Earth is written in scientific notation: 5,970,000,000,000,000,000,000,000 kg . Enter m and n , separated by commas.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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