Scientific Notation: Compressing Numbers

What is Scientific Notation?

Scientific Notation is a way of compressing too large or too small numbers. Scientists usually reformat and simplify colossal and infinitesimal numbers using scientific notation. For instance, rather than writing the distance between the Earth and the moon as 386,000km, we use its scientific notation: 3.86 × 10⁵. See much simpler conversions below:

9000 = 9 × 10³
540,000,000 = 5.4 × 10⁸

Converting a Number to Scientific Notation

When converting a number, leave one digit in front of the decimal point and count how many places it was moved to determine the exponent of 10. A scientific notation contains a coefficient, base, and exponent. The coefficient is the first number and it should always be equal or greater than 1 and less than 10. 

Converting Numbers Greater than 10:

Here’s how to convert a large number or a number greater than 10:

1. Move the decimal point to the left until you reach the first digit; place the decimal point after the first digit. 
2. Count how many places you moved the decimal point to the left.
3. The answer to Step 2 is the power of 10. 

Converting Numbers Smaller than 1:

Here’s how to convert numbers smaller than 1:

1. Move the decimal point to the right until you reach the first digit greater than 0.
2. Count how many places you moved the decimal point to the right.
3. The answer to Step 2 is the negative power of 10. 

REMEMBER: If you moved the decimal point to the right, the exponent should be negative.

Practice.

1. Write the scientific notation of 269.5.

Step 1. Move the decimal point two places to the left: 2.695
Step 2. How many places did you move the decimal point? 2. 
Step 3. Write 2 as the power of 10: 2.695×10²
Therefore, the answer is 2.695×10².

2. Write the scientific notation of .00000000387.

Step 1. Move the decimal point to the right until you reach the first digit greater than 0: 3.87
Step 2. How many places did you move the decimal point? 9. 
Step 3. Write 9 as the power of 10.
Since you moved the decimal point to the right, it should be a negative power: 3.87×10^-9.
Therefore, the answer is written as 3.87×10^-9.

3. What’s the scientific notation of 945,000,000,000?

Step 1. Move the decimal point to the left until after the first digit: 9.45
Step 2. How many places did you move the decimal point? 11. 
Step 3. Write 11 as the power of 10: 9.45×10¹¹.
Therefore, the answer is written as 9.45×10¹¹.

4. What’s the standard notation of 84.15×10⁷?

Step 1. The power (exponent) of 10 tells how many places the decimal point has to move to the right: 7. 
Step 2. Move the decimal point of the coefficient 7 places to the right.
Write zeroes in vacant places: 841,500,000
Therefore, the decimal notation of 84.15×10⁷ is 841,500,000.

Thank you for reading. We hope it’s effective! Always feel free to revisit this page if you ever have any questions about scientific notation

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