Question

Which is greater, 9 x 10-2 or 3 x 10-4? How many times

greater is the number you chose than the other number?
Explain your reasoning.​

Answer 1

`9 * 10^(-2 )(0.09)` is greater than
`3 * 10^(-4) (0.0003)`, and is 300 times greater.

Step-by-step explanation:

To determine which is greater between
`9 * 10^(-2 )` and
`3 * 10^(-4)`we need to understand how to interpret numbers in scientific notation. The expression
`9 * 10^(-2 )` means 9 times 1 following 2 zeroes to the left, resulting in 0.09. In the case of
`3* 10^(-4).` it means 3 times 1 following 4 zeroes to the left, producing 0.0003.

Comparing these values,
`9 * 10^(-2 )` is clearly the larger number because 0.09 is greater than 0.0003. To find out how many times greater it is, we divide the larger number by the smaller one: 0.09 / 0.0003 equals 300. Therefore,
`9 * 10^(-2 )`is 300 times greater than
`3* 10^(-4).`