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) 58 x 10⁶ km

2) 2.5 x 10⁻³ cm

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

Answer 2

1)
`5.8* 10^7\text{ km}`

2)
`2.5* 10^(-3)\text{ cm}`

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* 10^7`

We can remove the trailing zeros and add our unit:

`=5.8* 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* 10^(-3)`

Add our unit:

`=2.5* 10^(-3)\text{ cm}`

And we're done!