The number 9,136.67 written in scientific notation, is

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The question asks: 'The number 9,136.67 written in scientific notation, is' and provides four options. 
Option 1: '0.913667·10^3' translates to 0.913667 × 1000 = 913.667. This is not the intended scientific notation form for 9,136.67, and it also has a mantissa less than 1, which is not allowed in standard scientific notation.
Option 2: '0.913667·10^4' equals 0.913667 × 10,000 = 9,136.67. Although the numeric value matches, the mantissa is 0.913667, which is less than 1. In proper scientific notation, the mantissa (the number before the ×10) should be between 1 and 10, so this form is not standard.
Option 3: '9.13667·10^3' equals 9.13667 × 1000 = 9,136.67. Here the mantissa is 9.13667, which lies between 1 and 10, satisfying the conventional rule for scientific notation. This is the correctly formatted form.
Option 4: '9.13667·10^4' equals 9.13667 × 10,000 = 91,366.7. This represents a different value than 9,136.67, so it is incorrect in both value and typical scientific notation conventions.

In summary, two forms can represent 9,136.67 numerically (Option 2 and Option 3), but only Option 3 uses proper scientific notation with a mantissa between 1 and 10. The other forms either have a mantissa outside the [1, 10) range or produce a different value.

The number 9,136.67 written in scientific notation, is

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