Scientific Notation
Scientific notation is, essentially, a method for writing really big or really small numbers. It is called scientific notation because these huge numbers are often found in scientific work. For example, you might have the number 6000000000000. That’s really big, right? Unfortunately, it isn’t easy to tell exactly how big at first glance with all those zeroes stuck on the end. Instead, the number could be written as 6 * 1000000000000. Then you can change it.
Summary
Scientific notation is, essentially, a method for writing really big or really small numbers. It is called scientific notation because these huge numbers are often found in scientific work. For example, you might have the number 6000000000000. That’s really big, right? Unfortunately, it isn’t easy to tell exactly how big at first glance with all those zeroes stuck on the end. Instead, the number could be written as 6 * 1000000000000. Then you can change it.
Things to Remember
- Scientific notation is the way that scientists easily handle very large numbers or very small numbers.
- Scientific notation can be used to turn 0.0000053 into 5.3 x 10-6
- A power of ten with a positive exponent, such as 105, means the decimal was moved to the left.
- A power of ten with a negative exponent, such as 10-5, means decimal was moved to the right.
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Scientific Notation
Scientific Notation is used to handle very large or very small numbers. Scientists have developed a shorter method to express very large numbers. It is written as the product of a number (integer and decimal) and a power of 10.
Here are some examples of scientific notation.
| 10,000 = 1\(\times\)104 | 34,567 = 3.4567\(\times\) 104 |
| 1000 = 1\(\times\)103 | 495 = 4.95 \(\times\)102 |
| 10 = 1\(\times\)101 | 98 = 9.8 \(\times\)101(not usually done) |
| \(\frac{1}{10}\)=1\(\times\)10-1 | 0.23 = 2.3 \(\times\)10-1(not usually done) |
| \(\frac{1}{100}\)= 1\(\times\)10-2 | 0.026 = 2.6\(\times\)10-2 |
| \(\frac{1}{1000}\) = 1\(\times\)10-3 | 0.0064 =6.4\(\times\)10-3 |
| \(\frac{1}{10,000}\) = 1\(\times\)10-4 | 0.00088 = 8.8\(\times\)10-4 |
Example:
0.000457
= \(\frac{0.000457\times 1000000}{1000000}\)
=\(\frac{457}{10^6}\)
=457\(\times\) 10-6
=4.57\(\times\)102\(\times\)10-6
= 4.57\(\times\)10-4
Lesson
Real Number System
Subject
Compulsory Maths
Grade
Grade 8
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