Question

Express in standard form 0.0054 ad 2586.28

Answer 1

To express the numbers 0.0054 and 2586.28 in standard form (also known as scientific notation), we follow the format:

\[ a \times 10^n \]

where \( a \) is a number such that \( 1 \leq |a| < 10 \), and \( n \) is an integer.

1. For **0.0054**:
- Move the decimal point to the right until there's only one non-zero digit to the left of the decimal.
- We move the decimal point 3 places to the right:
- \( 0.0054 \) becomes \( 5.4 \).
- Since we moved the decimal point to the right, we represent this as:
\[
5.4 \times 10^{-3}
\]

2. For **2586.28**:
- Move the decimal point to the left until there's only one non-zero digit to the left of the decimal.
- We move the decimal point 3 places to the left:
- \( 2586.28 \) becomes \( 2.58628 \).
- Since we moved the decimal point to the left, we represent this as:
\[
2.58628 \times 10^{3}
\]

Thus, the standard form representations are:
- **0.0054**: \( 5.4 \times 10^{-3} \)
- **2586.28**: \( 2.58628 \times 10^{3} \)