0.0045 in scientific notation
Understand the Problem
The question is asking how to express the decimal number 0.0045 in scientific notation, which involves representing it as a number between 1 and 10 multiplied by a power of 10. To convert this, we would move the decimal point to the right until we have a number between 1 and 10, and then count how many places we moved it to determine the exponent.
Answer
The scientific notation of \( 0.0045 \) is \( 4.5 \times 10^{-3} \).
Answer for screen readers
The scientific notation of ( 0.0045 ) is ( 4.5 \times 10^{-3} ).
Steps to Solve
- Identify the Number Between 1 and 10
To express the decimal number ( 0.0045 ) in scientific notation, we first need to move the decimal point to the right to create a number between 1 and 10. Moving the decimal point right two places gives us ( 4.5 ).
- Count the Decimal Movement
Next, we need to count how many places we moved the decimal point. Since we moved it two places to the right, we will use an exponent of ( -2 ) (because moving to the right indicates a negative exponent).
- Combine into Scientific Notation
Now that we have the number and the exponent, we can express ( 0.0045 ) in scientific notation. It can be written as:
$$ 4.5 \times 10^{-3} $$
(Note: Since we moved to the right, we count the number of decimal places as a negative exponent).
The scientific notation of ( 0.0045 ) is ( 4.5 \times 10^{-3} ).
More Information
In scientific notation, the standard form is really useful for simplifying calculations and clearly expressing very large or very small numbers. The exponent provides information about the scale of the number, indicating how many places to move the decimal.
Tips
- Miscounting the decimal movement: It's easy to confuse how many places you move the decimal point. Always double-check the direction and count.
- Using a positive exponent for small numbers: Remember that for numbers less than 1, you'll have a negative exponent.
