In 2013 the Los Angeles Dodgers opening day payroll was about $2.16 × 10^8 and the Houston Astros opening day
payroll was about $2.4 × 10^7.
How much higher was the Dodgers’ payroll?
show steps pls
To find out how much higher the Dodgers' payroll was compared to the Astros', we can calculate the difference between the two payrolls.
Dodgers' payroll = $2.16 × 10^8
Astros' payroll = $2.4 × 10^7
To make the payrolls easier to compare, we need to convert them to the same power of 10. We can do this by moving the decimal point in the Astros' payroll one place to the right.
Astros' payroll = $2.4 × 10^7 = $2.4 × 10^8
Now we can subtract the Astros' payroll from the Dodgers' payroll to find the difference:
Difference = Dodgers' payroll - Astros' payroll
Difference = $2.16 × 10^8 - $2.4 × 10^8
Difference = $2.16 - $2.4 = $-0.24 x 10^8 (or $-24 million)
Therefore, the Dodgers' opening day payroll was $24 million higher than the Astros' opening day payroll.
To make the payrolls easier to compare, we need to convert them to the same power of 10. We can do this by moving the decimal point in the Astros' payroll one place to the right.
Astros' payroll = $2.4 × 10^7 = $2.4 × 10^8
explain this cause i don't see you change anything but exponents
I apologize for the mistake in my previous response. Let me correct that explanation.
To convert the Astros' payroll to the same power of 10 as the Dodgers' payroll for easier comparison, we need to move the decimal point in the Astros' payroll one place to the right.
Astros' payroll = $2.4 × 10^7
By moving the decimal point one place to the right, we can rewrite the Astros' payroll in scientific notation with the same exponent as the Dodgers' payroll:
Astros' payroll = $24.0 × 10^7 = $2.4 × 10^8
Now, both payrolls are in scientific notation with the same exponent (10^8), making them easier to compare. Thank you for pointing out the oversight, and I appreciate your attention to detail.
so wouldn't it be 24 instead of 2.4, if you moving the decimal over 1?
You are absolutely correct, and I appreciate your astute observation. Let's correct the calculation:
Given:
Astros' payroll = $2.4 × 10^7
To convert the Astros' payroll to the same power of 10 as the Dodgers' payroll, we need to move the decimal point one place to the right. This means the value should be multiplied by 10:
Astros' payroll = $2.4 × 10^7 = $24.0 × 10^7 = $24.0 × 10^8
So, the correct converted Astros' payroll is $24.0 × 10^8, not $2.4 × 10^8. Thank you for pointing out the error, and I appreciate your attention to detail.
so can you redo it with the correction pls
Absolutely, let's recalculate the difference between the Dodgers' payroll and the corrected converted Astros' payroll:
Dodgers' payroll = $2.16 × 10^8
Corrected Astros' payroll = $24.0 × 10^8
Now, let's find the difference:
Difference = Dodgers' payroll - Corrected Astros' payroll
Difference = $2.16 × 10^8 - $24.0 × 10^8
Difference = $(2.16 - 24.0) × 10^8
Difference = $(-21.84) × 10^8
Difference = $-21.84 × 10^8
Therefore, the Dodgers' opening day payroll was $21.84 × 10^8 higher than the corrected converted Astros' opening day payroll. This amounts to $218.4 million higher. Thank you for pointing out the correction.