Question

The average distance from the sun to the planet Mercury is about 58,000,000 km. The diameter of a
human hair is about 0.0025 cm. What is the distance from the sun to Mercury written in scientific notation? show your work on a peace of paper please~!

50+ points!~

Answer 1

Answer:

1) $5.8\times 10^7\text{ km}$

2) $2.5\times 10^{-3}\text{ cm}$

Step-by-step explanation:

To put a value into scientific notation, we need to:

1) Move to decimal place such that our new value is between 1 and 10 and

2) Multiply by 10^n, where n is the amount of spaces moved. If we moved to the left, n is positive. If we move to the right, n is negative.

1)

We have:

$58,000,000$

We can view this as:

$58,000,000.0$

Our new value should be between 1 and 10.

58000000

So, let's move our decimal 7 places to the left. This gives us:

$5.8000000$

Since we moved 7 to the left, we need to multiply by 10^7. Note that the 7 is positive. So:

$=5.8000000\times 10^7$

We can remove the trailing zeros and add our unit:

$=5.8\times 10^7\text{ km}$

2)

We have:

$0.0025$

Our new value should be between 1 and 10. So, move the decimal places 3 units to the right. This yields:

$2.5$

Since we moved 3 to the right, we need to multiply by 10^(-3). This time, note that our exponent is negative. So:

$=2.5\times 10^{-3}$

Add our unit:

$=2.5\times 10^{-3}\text{ cm}$

And we're done!

Answer 2

Answer: 1)  58 x 10⁶ km

2)  2.5 x 10⁻³ cm

Step-by-step explanation:

1. 58,000,000 km

2. 0.0025 cm

write in scientific notation:

1)

it would be more easier to read a notation in every 3 decimal places like thousands, millions, billions, etc.

we have 58,000,000 (note where the comma is placed) count every 3 to the left. just multiply by 10^6.

= 58 x 10⁶ km

2) 0.0025 (move 3 decimal places to the right)

= 2.5 x 10⁻³ cm