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Understanding significant digits (or significant figures) is essential to handle precision in scientific calculations. Significant digits indicate the precision of a measurement. For example, in the number 5.2, both 5 and 2 are significant digits. The digits convey how precise the measurement is.
When multiplying numbers, the number of significant digits in the final product should be the same as the number with the fewest significant digits used in your calculation. Like in our example, 5.2 and 2.6 both have two significant digits. So, our final answer must also have two significant digits.
Having a grasp of significant digits ensures that the representation of numbers doesn’t overstate the precision of the measurement.

When multiplying numbers in scientific notation, it’s crucial to manage the exponents properly. Scientific notation typically represents numbers as a product of a number (called the coefficient) and 10 raised to an exponent. Here’s the structure: \[ a \times 10^b \times c \times 10^d = (a \times c) \times 10^{(b+d)} \ \]
In our exercise, we had to multiply coefficients first: \[ 5.2 \times 2.6 = 13.52 \ \]
Then, we combined exponents by adding them: \[ 10^6 \times 10^4 = 10^{(6+4)} = 10^{10} \ \]
Finally, we combined these results into one expression: \[ 13.52 \times 10^{10} \ \]

Scientific notation is a way to simplify very large or very small numbers, making them easier to work with. The general form is: \[ N \times 10^n \ \]
Where \(N\) is a number between 1 and 10, and \(n\) is an integer. In our example, the calculated result was initially \[ 13.52 \times 10^{10} \ \]
But, for proper scientific notation, the coefficient must be between 1 and 10. So, we adjust it to: \[ 1.352 \times 10^{11} \ \]
Even after this adjustment, we have to apply significant digits, leading to the final answer: \[ 1.4 \times 10^{11} \ \]