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What is Engineering Notation? |
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What is engineering notation? Engineering notation is a method of writing really big and really small numbers. In engineering notation, the exponent must always be a multiple of three so that it is equivalent to a value represented by a metric prefix: | tera | T | 1,000,000,000,000 | 1012 | | giga | G | 1,000,000,000 | 109 | | mega | M | 1,000,000 | 106 | | kilo | k | 1,000 | 103 | | | 1 | 100 | | milli | m | 0.001 | 10¯3 | | micro | µ | 0.000001 | 10¯6 | | nano | n | 0.000000001 | 10¯9 | | pico | p | 0.000000000001 | 10¯12 |
How is engineering notation different from scientific notation? Engineering notation is written the same way as scientific notation, except that the exponent is always a multiple of three. Because of this, in engineering notation you have to move the decimal place at times. So while in scientific notation you always put the decimal after the first digit (such as 12300000 = 1.23 X 107), in engineering notation you move the decimal to accomodate the exponent needing to be a multiple of three. So the same number 12300000 in engineering notation would be displayed 12.3 X106. This is useful so we can attach a metric prefix to a quantity, such as 12.3 MB (Mega Bytes) and put numbers in to a language we can more easily understand. |
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Adding And Subracting Numbers with Scientific Notation |
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To add and subtract with scientific notation it is important to learn a couple terms, base and exponent. The number to the right is 2,400,000 represented in scientific notation. 2.4 is the base and 6 is the exponent (how many decimal places are added after the base number).
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Step By Step: Adding with Scientific Notation 1. In order to add or subtract exponents need to be the same value. For example if we were to add 2.4 X 106 + 1.2 X 107
we need to first get the exponents to be the same. Since the exponent refers to the number of decimal places, we can add (or subtract) a decimal place to the base number. How do we know which exponent to change--106 or 107? It doesn't really matter, the math will work out either way. However, scientific notation usually maintains no more than one digit before the decimal point. So that means we change our equation to read: .24 X 107 + 1.2 X 107
*note we haven't changed the number, we have just represented the same number differently (1.2 X 107 = 12,000,000 12 X 106=12,000,000) 2. The next step is to add the base numbers, the exponent stays the same. 2.4 X 106 + 12 X 106 =14.4 X 106 or, 14,400,000 Step By Step: Subtracting with Scientific Notation
1. Let's take the following problem: 1.3 X 104 - 3.4 X 103 First, we need to ge the exponents to be the same value. Let's take 1.3 X 104 and to make the exponent 103, we have to add a decimal place on to 1.3, making it 13 X 103. So now our problem reads:
13 X 103 - 3.4 X 103 2. Our next step then is to subtract the base numbers.
13 X 103 - 3.4 X 103= 9.6 X 103 (or 96,000)
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Basics of Scientific Notation |
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In working with electricity we often need to calculate really big or really small numbers. I always like to do things the easy way and scientific notation makes math easier to do. Below is a table showing how large and small numbers are converted to scientific notation including the metric prefixes that are often used when referring to them. When writing a number in scientific notation, you write the number so that there is one digit before the decimal point such as:
1,000 = 1.0 X 103 The 3 represents the number of decimal places (or how many zeros).
If you have a very small number, such as .00001, you count the number of decimal places just like before, but you express the exponent as a negative.
.00001= 1.0 X 10-5 Really Small Numbers Prefix # Notation
(deci) 1/10 = 1 x 10-1 (tenths)
(centi) 1/100 = 1 x 10-2 (hundredths)
(milli) 1/1000 = 1 x 10-3 (thousandths)
1/10000 = 1 x 10-4
1/100000 = 1 x 10-5
(micro) 1/1000000 = 1 x 10-6 (millionths)
1/10000000 = 1 x 10-7
1/100000000 = 1 x 10-8
(nano) 1/1000000000 = 1 x 10-9 (billionths)
1/10000000000 = 1 x 10-10 |
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Math for Electronics
