Use of Scientific Notation

Imagine you are studying a distant star. The star might be trillions of kilometers from Earth, while its light’s wavelength might be a tiny fraction of a meter.

Writing these numbers in ordinary form creates long rows of zeros, making them hard to compare or use in calculations.

Scientific notation solves this by writing numbers as a coefficient multiplied by 10 raised to an exponent. Here, the coefficient is at least 1 but less than 10. The exponent shows how many places the decimal point moves to create the coefficient.

If the number is greater than or equal to 10, like a star’s distance, the decimal point moves left until one nonzero digit remains to its left, creating the coefficient. The number of places it moves gives a positive exponent.

If the number lies between 0 and 1, like light’s wavelength, the decimal point moves right. The number of places it moves gives a negative exponent.

Once numbers are written in scientific notation, their exponents show scale. So, when you compare the distances of two stars, the larger exponent points to a greater distance. If the exponents are the same, the coefficients show which star is farther away.