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.
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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: \[ 5.4 \times 10^{-3} \]
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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: \( 2.58628 \times 10^{3} \)