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 with the same exponent?

Back

Add the coefficients and keep the exponent the same. For example, (2 x 10^5) + (3 x 10^5) = (2 + 3) x 10^5 = 5 x 10^5.

Front

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

Back

Convert one number to have the same exponent as the other, then add the coefficients. For example, (4.1 x 10^5) + (5.5 x 10^6) becomes (4.1 x 10^5) + (55 x 10^5) = 59.1 x 10^5 = 5.91 x 10^6.

Front

What is the standard form of a number?

Back

The standard form is the way of writing numbers without exponents. For example, 1.5 x 10^3 in standard form is 1500.

Front

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

Back

Move the decimal point in the coefficient to the right for positive exponents and to the left for negative exponents. For example, -5.6 x 10^-3 = -0.0056.

Front

What is the rule for multiplying numbers in scientific notation?

Back

Multiply the coefficients and add the exponents. For example, (5 x 10^6) * (5 x 10^7) = (5 * 5) x 10^(6+7) = 25 x 10^13.

Front

What is the rule for dividing 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 coefficient in scientific notation?

Back

The coefficient is the number in front of the power of ten. It must be greater than or equal to 1 and less than 10.

Front

How do you express 0.00056 in scientific notation?

Back

0.00056 can be expressed as 5.6 x 10^-4.

Front

What is the significance of the exponent in scientific notation?

Back

The exponent indicates how many places to move the decimal point. A positive exponent moves it to the right, while a negative exponent moves it to the left.