Sure, let's rewrite the number 52.64 in scientific notation.
1. Identify the coefficient and the exponent: Scientific notation expresses a number in the form [tex]\( a \times 10^n \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex] and [tex]\( n \)[/tex] is an integer.
2. Move the decimal point: We need to express 52.64 such that there is only one non-zero digit to the left of the decimal point. To do this, we move the decimal point one place to the left, which gives us 5.264.
3. Determine the exponent: Since we moved the decimal point one place to the left, we multiply by [tex]\( 10^1 \)[/tex] to compensate.
4. Round the coefficient if needed: Sometimes scientific notations are rounded to a specific number of significant figures. In this case, we round 5.264 to two decimal places, which is 5.26.
Thus, the number 52.64 in scientific notation is:
[tex]\[
5.26 \times 10^1
\][/tex]
