To convert the number 0.000376 to standard form, we need to express it as a product of a number between 1 and 10, and a power of 10.
Here is the step-by-step process:
1. Identify the significant figures: The significant figures in the number 0.000376 are 3, 7, and 6.
2. Place the decimal point: To create a number between 1 and 10, we place the decimal point immediately after the first significant figure. This gives us 3.76.
3. Determine the exponent: Count the number of places the decimal has moved from its original position to the new position. Originally, the decimal point is after five zeroes (including leading zeros).
- Moving from 0.000376 to 3.76 involves moving the decimal 4 places to the right. Therefore, the exponent is -4.
4. Combine the two parts: In standard form, the number is written as:
[tex]\[
\text{(Significant figures)} \times 10^{\text{(Exponent)}}
\][/tex]
In this case, it becomes:
[tex]\[
3.76 \times 10^{-4}
\][/tex]
However, considering significant digits' accuracy needs more precision for clarity in most scientific contexts, we round 3.76 to one decimal place.
5. Rounding and final expression: With one decimal place, 3.76 rounds to 3.8.
Therefore, the number 0.000376 written in standard form is:
[tex]\[
3.8 \times 10^{-4}
\][/tex]
