. 3:1–6 The letter to Sardis does not praise the community but admonishes its members to watchfulness, mutual support, and repentance (Rev 3:2–3). The few who have remained pure and faithful will share Christ's victory and will be inscribed in the book of life ( Rev 3:4 – 5 ).
- Content analysis of textual big data produced by new media, particularly social media and mobile devices has become popular. These approaches take a simplified view of language that ignores the complexity of semiosis, the process by which meaning is formed out of language.
- Identifiers must be meaningful, short, quickly and easily typed and easily read. Valid identifiers: total sum average x y mark1 x1 Invalid identifiers 1x - begins with a digit char - reserved word.
The exponent (or index or power) of a number says
how many times to use the number in a multiplication.
102 means 10 × 10 = 100
(It says 10 is used 2 times in the multiplication)
Example: 103 = 10 × 10 × 10 = 1,000
- In words: 103 could be called '10 to the third power', '10 to the power 3' or simply '10 cubed'
Example: 104 = 10 × 10 × 10 × 10 = 10,000
- In words: 104 could be called '10 to the fourth power', '10 to the power 4' or '10 to the 4'
You can multiply any number by itself as many times Scrapple 1 3 1 – free form mind mapping tools. as you want using this notation (see Exponents), but powers of 10 have a special use ..
Powers of 10
'Powers of 10' is a very useful way of writing down large or small numbers.
Garageband. Instead of having lots of zeros, you show how many powers of 10 will make that many zeros
Example: 5,000 = 5 × 1,000 = 5 × 103
5 thousand is 5 times a thousand. And a thousand is 103. So 5 times 103 = 5,000
Can you see that 103 is a handy way of making 3 zeros?
Scientists and Engineers (who often use very big or very small numbers) like to write numbers this way.
Example: The Mass of the Sun
The Sun has a Mass of 1.988 × 1030 kg.
It is too hard to write 1,988,000,000,000,000,000,000,000,000,000 kg
(And very easy to make a mistake counting the zeros!)
Example: A Light Year (the distance light travels in one year)
It is easier to use 9.461 × 1015 meters, rather than 9,461,000,000,000,000 meters
It is commonly called Scientific Notation, or Standard Form.
Other Way of Writing It
Sometimes people use the ^ symbol (above the 6 on your keyboard), as it is easy to type.
Example: 3 × 10^4 is the same as 3 × 104
- 3 × 10^4 = 3 × 10 × 10 × 10 × 10 = 30,000
Calculators often use 'E' or 'e' like this:
Example: 6E+5 is the same as 6 × 105
- 6E+5 = 6 × 10 × 10 × 10 × 10 × 10 = 600,000
Example: 3.12E4 is the same as 3.12 × 104
Textual 7 7 0 17 64
- 3.12E4 = 3.12 × 10 × 10 × 10 × 10 = 31,200
The Trick
While at first it may look hard, there is an easy 'trick':
Textual 7 7 0 12
The index of 10 says ..
..how many places to move the decimal point to the right.
Example: What is 1.35 × 104 ?
You can calculate it as: 1.35 x (10 × 10 × 10 × 10) = 1.35 x 10,000 = 13,500
But it is easier to think 'move the decimal point 4 places to the right' like this:
Negative Powers of 10
Negative? What could be the opposite of multiplying? Dividing!
A negative power means how many times to divide by the number.
Example: 5 × 10-3 = 5 ÷ 10 ÷ 10 ÷ 10 = 0.005
Just remember for negative powers of 10:
For negative powers of 10, move the decimal point to the left.
So Negatives just go the other way.
Example: What is 7.1 × 10-3 ?
Well, it is really 7.1 x (1/10 × 1/10 × 1/10) = 7.1 × 0.001 = 0.0071
But it is easier to think 'move the decimal point 3 places to the left' like this:
Try It Yourself
Enter a number and see it in Scientific Notation:
Now try to use Scientific Notation yourself:
Summary
The index of 10 says how many places to move the decimal point. Positive means move it to the right, negative means to the left. Example:
Textual 7 7 0 11
| Number | In Scientific Notation | In Words | |
| Positive Powers | 5,000 | 5 × 103 | 5 Thousand |
| Negative Powers | 0.005 | 5 × 10-3 | 5 Thousandths |
