Question

Ramsey measured the mass of two fleas. The first flea had a mass of 2.4 x 10 ^-4
grams, and the second flea had a mass of 3 x 10 ^ -4
grams. The sum of the masses of the two fleas can be expressed as b x 10^n
grams.

Select a number for each blank to make the sentence true.

The value of the coefficient b
in the sum expressed above is

, and the value of the exponent n
in the sum expressed above is

.

Answer 1

To find the sum of the masses of the two fleas expressed in the form \( b \times 10^n \), we can start by adding their masses:

1. First flea mass: \( 2.4 \times 10^{-4} \) grams
2. Second flea mass: \( 3.0 \times 10^{-4} \) grams

To add these two numbers, we can write them with the same power of 10:

\[
2.4 \times 10^{-4} + 3.0 \times 10^{-4}
\]

Both values already have the same exponent, so we can directly add the coefficients:

\[
(2.4 + 3.0) \times 10^{-4} = 5.4 \times 10^{-4}
\]

Now, we can express this sum in the form \( b \times 10^n \):

Here, \( b = 5.4 \) and \( n = -4 \).

Therefore, the values are:
- The value of the coefficient \( b \) in the sum expressed above is **5.4**.
- The value of the exponent \( n \) in the sum expressed above is **-4**.