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