To write 0.00503 in scientific notation, we need to express it as a product of a number between 1 and 10 and a power of 10. Here are the steps to do this:
1. Identify the significant digits: For 0.00503, the significant digits are 5.03.
2. Determine the position of the decimal point: Originally, the decimal point is placed after the leading zeros and just before the 5 in 0.00503.
3. Move the decimal point: To transform the number into scientific notation, move the decimal point to the right of the first significant digit (in this case, the number 5). This gives us:
[tex]\[
5.03
\][/tex]
4. Count the positions moved: To determine the exponent, count how many places you moved the decimal point to position it immediately after the first non-zero digit. In the number 0.00503, we moved the decimal 3 places to the right:
[tex]\[
0.00503 \rightarrow 5.03
\][/tex]
5. Determine the exponent: Since we moved the decimal point 3 places to the right, the power of 10 will be negative (because the original number is less than 1). Therefore, the exponent is -3.
Putting this all together, the number 0.00503 can be written in scientific notation as:
[tex]\[
5.03 \times 10^{-3}
\][/tex]
The power of 10, when 0.00503 is written in scientific notation, is [tex]\(-3\)[/tex].
