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Number conversion in scientific notation involves changing a standard number into an easier-to-read format. This is especially useful for handling very large or very small numbers, like the distance between stars or the size of an atom.
In scientific notation, we always aim to express the number as a product of two parts:

• A number between 1 and 10
• A power of 10

For example, to convert 1,290,000, follow these steps:
-Identify the first non-zero digit (which is 1 in this case).
-Move the decimal point to just after this digit, forming 1.29.
-Count the number of places the decimal point moved (6 places to the left in this case).
-Combine the number and the power of ten: \(1.29 \times 10^6\)
Each step in the conversion process helps to transform unwieldy numbers into a compact, easily understandable format.

Understanding 'powers of ten' is key to mastering scientific notation. The power of ten indicates how many times you multiply 10 by itself. For example, 10^3 means 10 * 10 * 10 = 1000.
Here's a quick guide to the powers of ten:
- A positive exponent (e.g., 10^6) means you're multiplying by 10 repeatedly (one million in this case).
- A negative exponent (e.g., 10^-3) means you're dividing by 10 repeatedly (0.001 in this case).
In our examples:

• 1,290,000 becomes \(1.29 \times 10^6\), moving the decimal left makes it a positive exponent.
• 0.00000103 becomes \(1.03 \times 10^{-6}\), moving the decimal right makes it a negative exponent.

By converting to powers of ten, you simplify the arithmetic and comparisons of large and small numbers.

The core of scientific notation is moving the decimal point.
The direction and number of places you move the decimal point determine the exponent in the power of ten.
- For large numbers, move the decimal point to the left. Each move to the left increases the exponent by one.
- For small numbers, move the decimal point to the right. Each move to the right decreases the exponent (makes it more negative) by one.
Take, for instance, 1,290,000:
- Original number: 1,290,000
- Move the decimal point 6 places to the left: 1.290000
- Become: \(1.29 \times 10^6\)
Now consider 0.00000103:
- Original number: 0.00000103
- Move the decimal point 6 places to the right: 1.03
- Become: \(1.03 \times 10^{-6}\)
By mastering decimal point movement, you can effectively convert any number into scientific notation.