Scientific Notation Operations

Front

What is scientific notation?

Back

A way to express very large or very small numbers using powers of ten. It is written in the form a x 10^n, where 1 ≤ a < 10 and n is an integer.

Front

How do you add numbers in scientific notation with the same exponent?

Back

Add the coefficients (the numbers in front) and keep the exponent the same. For example, (5.3 x 10^5) + (3.7 x 10^5) = (5.3 + 3.7) x 10^5 = 9.0 x 10^5.

Front

What is the rule for multiplying numbers in scientific notation?

Back

Multiply the coefficients and add the exponents. For example, (3.4 x 10^5) * (1.2 x 10^-3) = (3.4 * 1.2) x 10^(5 + (-3)) = 4.08 x 10^2.

Front

How do you divide numbers in scientific notation?

Back

Divide the coefficients and subtract the exponents. For example, (9 x 10^-6) / (3 x 10^-3) = (9 / 3) x 10^(-6 - (-3)) = 3 x 10^-3.

Front

What is the process for subtracting numbers in scientific notation with the same exponent?

Back

Subtract the coefficients and keep the exponent the same. For example, (5 x 10^8) - (3.4 x 10^8) = (5 - 3.4) x 10^8 = 1.6 x 10^8.

Front

What is the significance of the exponent in scientific notation?

Back

The exponent indicates the power of ten by which the coefficient is multiplied, determining the scale of the number.

Front

How do you convert a number from standard form to scientific notation?

Back

Move the decimal point in the number until only one non-zero digit remains to the left. Count the number of places moved; this becomes the exponent of ten.

Front

What is the scientific notation for 0.00056?

Back

5.6 x 10^-4.

Front

What is the scientific notation for 4500000?

Back

4.5 x 10^6.

Front

How do you handle different exponents when adding or subtracting in scientific notation?

Back

Convert the numbers to have the same exponent before adding or subtracting. Adjust the coefficients accordingly.