A city has two water towers. One tower holds 7.35×10^5 gallons of water. The other holds 9.78×10^5

Question

gallons of water. What is the combined water capacity in Scientific Notation?

options:

1.713×10^6

7.1883×10^26

2.43×10^5

7.1883×10^11

Answer 1

To find the combined water capacity of the two water towers, we need to add the capacities in scientific notation.

The two capacities are:

• Tower 1: \( 7.35 \times 10^5 \) gallons
• Tower 2: \( 9.78 \times 10^5 \) gallons

When adding numbers in scientific notation, you must ensure both numbers have the same exponent. In this case, both numbers have the exponent \( 10^5 \), so we can directly add the coefficients:

\[ 7.35 + 9.78 = 17.13 \]

Now, we can express this sum in scientific notation. Since \( 17.13 \) is greater than \( 10 \), we need to convert it to proper scientific notation:

\[ 17.13 = 1.713 \times 10^1 \]

Now, we combine it with \( 10^5 \):

\[ 1.713 \times 10^1 \times 10^5 = 1.713 \times 10^{1+5} = 1.713 \times 10^6 \]

Thus, the combined water capacity in scientific notation is:

\[ \boxed{1.713 \times 10^6} \]

This matches option 1 in your list.