Question

Galaxy A has 8 × 10^8 stars. Galaxy B has 6 x 10^10 stars. Choose which galaxy has more stars. Then fill in the blank with a number written in standard notation.

Answer 1

So the complete answer is:

Galaxy B has more stars.

Galaxy B has 75 times as many stars as Galaxy A.

To solve the problem shown in your image, we need to compare the number of stars in Galaxy A and Galaxy B. The image says:

- Galaxy A has
`\( 8 * 10^(18) \)` stars.

- Galaxy B has
`\( 6 * 10^(20) \)` stars.

To determine which galaxy has more stars, we can compare the exponents of the powers of 10, since these will determine the size of the numbers.

Galaxy B has a power of
`\( 10^(20) \)`compared to Galaxy A's
`\( 10^(18) \).`Regardless of the coefficients (6 for Galaxy B and 8 for Galaxy A), the exponent on Galaxy B's number is higher, which means it has more stars because
`\( 10^(20) \)`is 100 times larger than
`\( 10^(18) \).`

Now to express how many times more stars Galaxy B has compared to Galaxy A, we divide the number of stars in Galaxy B by the number of stars in Galaxy A:

`\[ (6 * 10^(20))/(8 * 10^(18)) \]`

To do this, we can calculate the division by separating the coefficients and the powers of 10.

First, divide the coefficients (6 divided by 8).

Second, subtract the exponents of the powers of 10, because when you divide numbers in scientific notation, you subtract the exponents:

`\[ 10^(20) / 10^(18) = 10^(20-18) = 10^2 \]`

Now, let's do the math to find the exact number.

Galaxy B has 75 times as many stars as Galaxy A.

Answer 2

Given:

Galaxy A has 8 × 10^8 stars. Galaxy B has 6 x 10^10 stars.

We will write the numbers multiplied by ten raised to the same exponent

so,

`\begin{gathered} 8*10^8=8*10^8 \\ 6*10^(10)=6*100*10^8=600*10^8 \end{gathered}`

now, we will compare the numbers: 8 and 600

It is clear 600 is greater than 8

so, the answer will be option Galaxy B

Divide the number of stars of B by A

So,

`(6*10^(10))/(8*10^8)=(600*10^8)/(8*10^8)=(600)/(8)=75`

Galaxy B has 75 times as many stars as Galaxy A