Question

compare the two numbers to find which is greater. explain how you can compare them without writing them in standard notation first. 4.5×10^6 2.1×10^8

Answer 1

The number with the largest exponent is the largest value overall. In this case, that would be 2.1 x 10^8 which is the largest value since 8 is the largest exponent.

Note: The number 4.5 x 10^6 is the number 4.5 million, while the number 2.1 x 10^8 is the number 210 million. The positive exponent means "move the decimal point that number of times to the right". So 4.5 x 10^6 means "move the decimal point 6 spots to the right" so you can convert to standard form. The larger the exponent, the more places the decimal point moves to the right.