Compare numbers written in scientific notation

key notes :

You can compare two numbers written in scientific notation by following these steps:

  1. Compare the powers of 10. If one of the powers of 10 is greater than the other, that number is greater.
  2. If the powers of 10 are the same, compare the first factors. If one of the first factors is greater than the other, that number is greater.

Let’s try it! Compare 4.7×10⁸ and 3.6×10⁹.

Start by comparing the powers of 10. Since 10⁸ < 10⁹, then 4.7×10⁸ < 3.6×10⁹.

You can see why this works by rewriting each number in standard form.

  • 4.7×10⁸ = 470,000,000
  • 3.6×10⁹ = 3,600,000,000

🏹Since 470,000,000<3,600,000,000, then 4.7×10⁸ < 3.6×10⁹.

Another example:

Compare 5.1×10⁻⁷ and 2.8×10⁻⁷.

Start by comparing the powers of 10. Since they are the same, compare the first factors.

Compare the first factor in each number. Since 5.1>2.8, then 5.1×10⁻⁷>2.8×10 ⁻⁷.

You can see why this works by rewriting each number in standard form.

  • 5.1×10⁻⁷ = 0.00000051
  • 2.8×10⁻⁷ = 0.00000028

🏹Since 0.00000051 > 0.00000028, then 5.1×10⁻⁷ > 2.8×10⁻⁷

Learn with an example

Which sign makes the statement true?

Both numbers are in correct scientific notation, so you can compare them.

Look at the powers of 10.

2.95 × 103  ? 2.95 × 101

​103 is larger than 101, so the first number is larger.

2.95 × 103 > 2.95 × 101

Which sign makes the statement true?

Express the second number in standard form. Look at 104. The 10 is raised to the power of 4. You want to move the decimal point 4 places to the right. First, write extra zeroes to the right of the decimal point. Remember that writing extra zeroes to the right of a decimal does not change its value.

3.86 = 3.8600

Now move the decimal point 4 places to the right.

3.8600 → 38,600.

3.86 × 104 = 38,600

Compare the two numbers.

38,600 = 38,600

38,600 = 3.86 × 104

Which sign makes the statement true?

Both numbers are in correct scientific notation, so you can compare them.

Look at the powers of 10.

1.4 × 104 ? 1.4 × 103

​104 is larger than 103, so the first number is larger.

1.4 × 104 > 1.4 × 103

Let’s practice!