Adding and Subtracting in Scientific Notation

Front

What is scientific notation?

Back

A way of expressing numbers as a product of a coefficient and a power of 10, typically 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

Simply add the coefficients and keep the exponent the same. For example, (2.6 x 10^6) + (4.2 x 10^6) = (2.6 + 4.2) x 10^6 = 6.8 x 10^6.

Front

What is the first step in adding numbers in scientific notation with different exponents?

Back

Convert the numbers to have the same exponent before adding the coefficients.

Front

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

Back

Subtract the coefficients and keep the exponent the same. For example, (9.87 x 10^7) - (7.42 x 10^7) = (9.87 - 7.42) x 10^7 = 2.45 x 10^7.

Front

What is the process for subtracting numbers in scientific notation with different exponents?

Back

Convert the numbers to have the same exponent before subtracting the coefficients.

Front

How do you multiply numbers in scientific notation?

Back

Multiply the coefficients and add the exponents. For example, (2 x 10^3) * (3 x 10^4) = (2 * 3) x 10^(3+4) = 6 x 10^7.

Front

How do you divide numbers in scientific notation?

Back

Divide the coefficients and subtract the exponents. For example, (3 x 10^-5) / (4 x 10^2) = (3/4) x 10^(-5-2) = 0.75 x 10^-7.

Front

What is the significance of the coefficient in scientific notation?

Back

The coefficient must be between 1 and 10 to maintain the standard form of scientific notation.

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 10.

Front

What is the rule for exponents when adding or subtracting in scientific notation?

Back

Only the coefficients are added or subtracted; the exponents must be the same.