Comparing numbers in scientific notation

Scientific notation makes it quick to compare sizes, because the exponent already tells you how big a number is.

Compare the exponents first

If two numbers are both in scientific notation, the one with the larger exponent is larger. For example 3 × 10⁵ is bigger than 9 × 10⁴, because 10⁵ is ten times 10⁴ — the smaller coefficient does not matter once the exponent is bigger.

If the exponents are equal

When the exponents match, compare the coefficients. So 4.1 × 10⁶ is larger than 3.8 × 10⁶, because 4.1 > 3.8.

A quick check

You can always expand both numbers to standard form if you are unsure — but with practice the exponent-first method is much faster.

Three rules that always help

• Bigger exponent means bigger number.
• Equal exponents → compare the coefficients.
• When in doubt, expand both to standard form and compare.

Keep going

• Practice: Compare scientific notation
• Back to the scientific notation overview