Comparing Scientific Notation

Examples

5.21 * 10^{3}

5.21 * 10^{2}

First we need to convert

5.21 * 10^{3}

to standard notation

Exponent is positive, so move decimal point right

5.210 => 52.10

52.10 => 521.0

521.0 => 5210.

5.21 * 10^{3} equals 5{,}210 in decimal

Compare the two numbers

5,210 > 521

2.43 * 10^{5}

5.21 * 10^{5}

Compare the powers of 10

The exponents are both 5, so we need to compare the coefficients

2.43 is less than 5.21

Therefore the first number is less than the second number

1.11 * 10^{-2}

1.54 * 10^{-3}

First we need to convert

1.11 * 10^{-2}

to standard notation

Exponent is negative, so move decimal point left

1.11 => .111

.111 => .0111

1.11 * 10^{-2} equals 0.0111 in decimal

Compare the two numbers

0 > 0

5.21 * 10^{3}

5.21 * 10^{2}

Compare the powers of 10

The exponent in the first number (3) is greater than the exponent in the second number (2)

Therefore the first number is greater than the second number