Make sure to watch the following video to learn how to avoid a common calculator error when working with scientific notation. Show Scientific Notation (also called Standard Form in Britain) is a special way of writing numbers: It makes it easy to use big and small values. Why is 700 written as 7 × 102 in Scientific Notation ? 700 = 7 × 100 and 100 = 102 (see powers of 10) so 700 = 7 × 102 Both 700 and 7 × 102 have the same value, just shown in different ways.
1,000,000,000 = 109 , The number is written in two parts:
In this example, 5326.6 is written as 5.3266 × 103, because 5326.6 = 5.3266 × 1000 = 5.3266 × 103 Try It YourselfEnter a number and see it in Scientific Notation: Now try to use Scientific Notation yourself: Other Ways of Writing It3.1 × 10^8 We can use the ^ symbol (above the 6 on a keyboard), as it is easy to type.
Example: 3 × 10^4 is the same as 3 × 104
Calculators often use "E" or "e" like this:
Example: 6E+5 is the same as 6 × 105
Example: 3.12E4 is the same as 3.12 × 104
To figure out the power of 10, think "how many places do I move the decimal point?"
But it is now in Scientific Notation Check!After putting the number in Scientific Notation, just check that:
Why Use It?Because it makes it easier when dealing with very big or very small numbers, which are common in Scientific and Engineering work.
Example: it is easier to write (and read) 1.3 × 10-9 than 0.0000000013 It can also make calculations easier, as in this example:
Example: a tiny space inside a computer chip has been measured to be 0.00000256m wide, 0.00000014m long and 0.000275m high. What is its volume? Let's first convert the three lengths into scientific notation:
Then multiply the digits together (ignoring the ×10s): 2.56 × 1.4 × 2.75 = 9.856 Last, multiply the ×10s: 10-6 × 10-7 × 10-4 = 10-17 (easier than it looks, just add −6, −4 and −7 together) The result is 9.856×10-17 m3 It is used a lot in Science:
The Sun has a Mass of 1.988 × 1030 kg. Easier than writing 1,988,000,000,000,000,000,000,000,000,000 kg
It can also save space! Here is what happens when you double on each square of a chess board: Values are rounded off, so 53,6870,912 is shown as just 5×108 That last value, shown as 9×1018 is actually 9,223,372,036,854,775,808 Engineering NotationEngineering Notation is like Scientific Notation, except that we only use powers of ten that are multiples of 3 (such as 103, 10-3, 1012 etc). Examples:
Example: 0.00012 is written 120 × 10-6Notice that the "digits" part can now be between 1 and 1,000 (it can be 1, but never 1,000). The advantage is that we can replace the ×10s with Metric Numbers. So we can use standard words (such as thousand or million), prefixes (such as kilo, mega) or the symbol (k, M, etc)
Example: 19,300 meters is written 19.3 × 103 m, or 19.3 km
Example: 0.00012 seconds is written 120 × 10-6 s, or 120 microseconds Copyright © 2020 MathsIsFun.com
Multiplying a decimal by 10 moves the decimal point one place to the right. Dividing a decimal by 10 moves the decimal point one place to the left. Multiplying or dividing by a power of 10 will move the decimal point equal to the number of 0s. |