Scientific Notation Operations

Front

What is scientific notation?

Back

A way to express very large or very small numbers using powers of ten. For example, 3000 can be written as 3 x 10^3.

Front

How do you add numbers in scientific notation?

Back

Align the exponents. If they are different, convert one number to have the same exponent as the other before adding.

Front

What is the standard form of a number?

Back

A way of writing numbers without exponents, showing all digits. For example, 5.6 x 10^-3 in standard form is 0.0056.

Front

How do you subtract numbers in scientific notation?

Back

Align the exponents. Convert one number to have the same exponent as the other if necessary, then subtract the coefficients.

Front

What is the product of two numbers in scientific notation?

Back

Multiply the coefficients and add the exponents. For example, (2 x 10^3) * (3 x 10^2) = 6 x 10^(3+2) = 6 x 10^5.

Front

What is the quotient of two numbers in scientific notation?

Back

Divide the coefficients and subtract the exponents. For example, (6 x 10^6) / (2 x 10^3) = 3 x 10^(6-3) = 3 x 10^3.

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 significance of the exponent in scientific notation?

Back

The exponent indicates how many times to multiply the base (10) by itself, determining the scale of the number.

Front

What happens when you multiply a number in scientific notation by 10?

Back

You increase the exponent by 1. For example, (4 x 10^5) * 10 = 4 x 10^(5+1) = 4 x 10^6.

Front

What is the result of (5.2 x 10^7) + (3.01 x 10^4)?

Back

5.20301 x 10^7 (after converting 3.01 x 10^4 to the same exponent).