Which sign makes the statement true?

0.000090 × 10^–10 9.0 × 10^–14

1 answer

To determine which sign makes the statement true between \(0.000090 \times 10^{-10}\) and \(9.0 \times 10^{-14}\), we can convert both numbers into the same format for comparison.

  1. Convert \(0.000090\) to scientific notation: \[ 0.000090 = 9.0 \times 10^{-5} \]

  2. Therefore, we rewrite \(0.000090 \times 10^{-10}\): \[ 0.000090 \times 10^{-10} = (9.0 \times 10^{-5}) \times 10^{-10} = 9.0 \times 10^{-15} \]

Now we have the two numbers for comparison:

  • \(9.0 \times 10^{-15}\) (which is \(0.000090 \times 10^{-10}\))
  • \(9.0 \times 10^{-14}\)

Now we can compare \(9.0 \times 10^{-15}\) and \(9.0 \times 10^{-14}\): Since \(9.0 \times 10^{-14}\) is greater than \(9.0 \times 10^{-15}\):

Thus, the correct comparison is:

\[ 0.000090 \times 10^{-10} < 9.0 \times 10^{-14} \]

So the statement is true with the "<" sign.