10.7 Operations with scientific notation

Front

What is scientific notation?

Back

A way of expressing numbers as a product of a coefficient and a power of 10, e.g., a × 10^n.

Front

How do you multiply numbers in scientific notation?

Back

Multiply the coefficients and add the exponents: (a × 10^m) × (b × 10^n) = (a × b) × 10^(m+n).

Front

How do you divide numbers in scientific notation?

Back

Divide the coefficients and subtract the exponents: (a × 10^m) / (b × 10^n) = (a / b) × 10^(m-n).

Front

What is the purpose of using scientific notation?

Back

To simplify the representation of very large or very small numbers, making calculations easier.

Front

How do you add numbers in scientific notation with different exponents?

Back

Convert to the same exponent, then add the coefficients: a × 10^m + b × 10^n = (a × 10^(n-m) + b) × 10^n if m < n.

Front

What is the smallest number among 1.3 x 10^20, 2.9 x 10^21, 9.5 x 10^32, and 8.4 x 10^19?

Back

8.4 x 10^19.

Front

What is the largest number among 4.8 x 10^-6, 1.3 x 10^20, 3.1 x 10^-4, 9.2 x 10^-5, 9.5 x 10^32, 5.9 x 10^-5, 2.9 x 10^21, and 8.4 x 10^19?

Back

9.5 x 10^32.

Front

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

Back

Move the decimal point to create a number between 1 and 10, then count the number of places moved to determine the exponent.

Front

What is the result of (2.1 x 10^2) × (3.0 x 10^4)?

Back

6.3 x 10^6.

Front

What is the result of (6.9 x 10^7) / (2.3 x 10^-3)?

Back

3 x 10^10.