A Guide to the GRE/Scientific Notation

Scientific Notation

In scientific notation, move the number left of the units digit once for each power of 10, or right of the decimal point for each negative power of 10.

1.76642 x 10¹⁸ = 1,766,420,000,000,000,000

1.76642 x 10⁻¹⁸ = .0000000000000000176642

Scientific notation is a method of expressing very large or very small numbers. It consists of a single number multiplied by a power of 10.

Practice

1. What is 18,221 expressed in scientific notation?

2. What is 6.5438 x 1011 expressed in conventional notation?

3. Express .0000652 in scientific notation.

Answers to Practice Questions

1. 1.8221 x 104

Move the decimal place to the left of the first number, then multiply by a power of 10 for each place you slid it to the right, or by a negative power of 10 for each place you slid it to the left.

2. 654,380,000,000

Slide the decimal place to the right once for each power of ten. Add a zero if there is no number to slide.

3. 6.52 x 10-5

Move the decimal place to the left of the first number, then multiply by a power of 10 for each place you slid it to the right, or by a negative power of 10 for each place you slid it to the left.