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Lab 1 - CONVERSION BETWEEN SCIENTIFIC AND DECIMAL NOTATION

This Virtual Astronomy Laboratory Unit presents an introduction to scientific notation for writing the very large numbers which are frequently encountered in astronomy. The first two exercises illustrate the mathematics of arithmetic using scientific notation, and the last two use numbers in scientific notation in examples which focus on the vastness of space and the time it would take to complete a journey to a heavenly object.

Converting Numbers between Decimal and Scientific Notations Numbers which are very large or very small are inconvenient to write in decimal notation. Instead, scientific notation is commonly used, where the number is written as a power of 10 in the form of a mantissa and an exponent:

m x 10e

where the mantissa (m) is a decimal number between 1. 0 and 9. 999. .. ., and the exponent (e) is an integer. To write numbers using scientific notation, move the decimal point until only one digit appears to the left of the decimal point. Count the number of places the decimal point was moved and use that number as the exponent. Numbers greater than 1 have a positive exponent, numbers less than 1 have a negative exponent.

EXAMPLES

38, 000, 000 is written as 3. 8 x 107. 280. 6 is written as 2. 806 x 102. 0. 0000000506 is written as 5. 06 x 10-8.

EXERCISE

Select Converting Numbers from the list of exercises. In the window which opens up you can choose to have the computer: a. generate a number in scientific format for you to convert to decimal format b. generate a number in decimal format for you to convert to scientific format c. generate numbers in a random format for you to convert to the other format Enter your answer using the numbers keys on the keyboard. If you are entering a number in scientific format, typing an x or an e will change from the mantissa to the exponent. If you make a mistake press the back arrow key (3) to erase the last digit in the number.

After you have entered your number, select the button labeled Check your answer. If the computer indicates your answer is wrong, then you should use the back arrow key (3) to modify your answer and check it again.

Arithmetic in Scientific Notation Multiplication and division in scientific notation follow two simple rules:

When multiplying two numbers, multiply the mantissas and add the exponents. When dividing two numbers, divide the mantissa of the numerator by that of the denominator, and subtract the exponent of the denominator from that of the numerator. EXAMPLES (3. 2x104)x(2. 6x109)=(3. 2x2. 6)x10(4+9) =8. 32x1013 (7. 9x106)(5. 4x1014)=(7. 95. 4)x10(6-14) =1. 46x10-8 (3. 1 x 1015) (8. 54 x 10-14) = (3. 1 8. 54) x 10(15-(-14)) = 0. 531 x 1029 = 5. 31 x 1028 EXERCISESelect Arithmetic in Scientific Notation from the list of exercises. In the window which opens up you can choose to have the computer:

a. generate a multiplication problem b. generat...

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