Scientific Notation and Operations in Scientific Notation

Front

What is scientific notation?

Back

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

Front

How do you multiply numbers in scientific notation?

Back

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

Front

What is the result of (5 x 10^6) (5 x 10^7)?

Back

2.5 x 10^14.

Front

If the exponent in scientific notation is positive, what does it indicate about the original number?

Back

It indicates that the original number is a really big number.

Front

How do you multiply (2.1×10^2) × (3.0×10^4)?

Back

Multiply the coefficients: 2.1 × 3.0 = 6.3, and add the exponents: 2 + 4 = 6, so the result is 6.3 x 10^6.

Front

What is the area of a rectangular region with length 10,000 meters and width 4.8 × 10^3 meters in scientific notation?

Back

4.8 x 10^7 square meters.

Front

How do you convert 0.068 into scientific notation?

Back

Move the decimal point two places to the right to get 6.8, and since the decimal moved two places, the exponent is -2, so it is 6.8 x 10^-2.

Front

What is the result of (3 x 10^5) + (4 x 10^5)?

Back

7 x 10^5.

Front

What is the result of (6 x 10^3) / (2 x 10^1)?

Back

3 x 10^2.

Front

What does it mean if a number is expressed as 1.2 x 10^-3?

Back

It means the number is 0.0012.