To express the number 0.37 in expanded form using powers of 10, we break it down into its decimal components.
The number 0.37 can be decomposed as:
- The digit 3 is in the tenths place, which corresponds to \(3 \times 10^{-1}\) (or \(3 \times \frac{1}{10}\)).
- The digit 7 is in the hundredths place, which corresponds to \(7 \times 10^{-2}\) (or \(7 \times \frac{1}{100}\)).
So, you can fill in the blanks as follows:
0.37 (3 × 10^{-1}) + (7 × 10^{-2})
This expands the number 0.37 into its component parts expressed in terms of powers of 10.