Math / Numbers & Operations

QuestionFor the following conversion: $6 \times 10^{-1} \mathrm{~km}=? \mathrm{~nm}$
In order, in the blanks below:
1. Report the orders of magnitude between the two prefixes. Report as a positive number. For instance there are 10 orders of magnitude between deci and giga.
2. Write the conversion factor. For instance $1 \mathrm{~kg} / 10^{\wedge} 3 \mathrm{~g}$
3. Write the final answer. If the conversion is given in scientific notation, write the answer in scientific notation, using the correct number of significant digits.

Studdy Solution

STEP 1

What is this asking? We need to figure out how many nanometers are in $6 \times 10^{-1}$ kilometers! Watch out! Prefixes can be tricky!
Double-check those exponents, they can easily trip you up.

STEP 2

1. Magnitude Difference
2. Conversion Factor
3. Calculate Nanometers

STEP 3

We're going from kilometers to nanometers.
Remember, kilo means $10^3$ and nano means $10^{-9}$ .

STEP 4

To find the magnitude difference, we're looking at the difference between 3 and -9.
That's $3 - (-9) = 3 + 9 = \mathbf{12}$ .
So, there's a 12 order of magnitude difference between kilo and nano.

STEP 5

Since 1 kilometer is the same as $10^{12}$ nanometers, our conversion factor is $\frac{10^{12} \text{ nm}}{1 \text{ km}}$ .
We put nanometers on top because that's what we want to end up with!

STEP 6

Alright, let's multiply our initial value by our conversion factor: $6 \times 10^{-1} \text{ km} \cdot \frac{10^{12} \text{ nm}}{1 \text{ km}}$

STEP 7

Notice how the km units divide to one, leaving us with just nanometers.
Awesome! Now we just have: $6 \times 10^{-1} \cdot 10^{12} \text{ nm}$

STEP 8

Let's combine those exponents: $-1 + 12 = 11$ . $6 \times 10^{11} \text{ nm}$

STEP 9

1. 12
2. $\frac{10^{12} \text{ nm}}{1 \text{ km}}$
3. $6 \times 10^{11} \text{ nm}$

Was this helpful?

Studdy Solution

STEP 1

What is this asking? We need to figure out how many nanometers are in $6 \times 10^{-1}$ kilometers! Watch out! Prefixes can be tricky!
Double-check those exponents, they can easily trip you up.

STEP 2

1. Magnitude Difference
2. Conversion Factor
3. Calculate Nanometers

STEP 3

We're going from kilometers to nanometers.
Remember, kilo means $10^3$ and nano means $10^{-9}$ .

STEP 4

To find the magnitude difference, we're looking at the difference between 3 and -9.
That's $3 - (-9) = 3 + 9 = \mathbf{12}$ .
So, there's a 12 order of magnitude difference between kilo and nano.

STEP 5

Since 1 kilometer is the same as $10^{12}$ nanometers, our conversion factor is $\frac{10^{12} \text{ nm}}{1 \text{ km}}$ .
We put nanometers on top because that's what we want to end up with!

STEP 6

Alright, let's multiply our initial value by our conversion factor: $6 \times 10^{-1} \text{ km} \cdot \frac{10^{12} \text{ nm}}{1 \text{ km}}$

STEP 7

Notice how the km units divide to one, leaving us with just nanometers.
Awesome! Now we just have: $6 \times 10^{-1} \cdot 10^{12} \text{ nm}$

STEP 8

Let's combine those exponents: $-1 + 12 = 11$ . $6 \times 10^{11} \text{ nm}$

STEP 9

1. 12
2. $\frac{10^{12} \text{ nm}}{1 \text{ km}}$
3. $6 \times 10^{11} \text{ nm}$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

What is this asking? We need to figure out how many nanometers are in 6×10−16 \times 10^{-1}6×10−1 kilometers! Watch out! Prefixes can be tricky!Double-check those exponents, they can easily trip you up.

STEP 2

1. Magnitude Difference2. Conversion Factor3. Calculate Nanometers

STEP 3

We're going from **kilometers** to **nanometers**.Remember, **kilo** means 10310^3103 and **nano** means 10−910^{-9}10−9.

STEP 4

To find the **magnitude difference**, we're looking at the difference between 3 and -9.That's 3−(−9)=3+9=123 - (-9) = 3 + 9 = \mathbf{12}3−(−9)=3+9=12.So, there's a **12 order of magnitude** difference between kilo and nano.

STEP 5

Since 1 kilometer is the same as 101210^{12}1012 nanometers, our **conversion factor** is 1012 nm1 km \frac{10^{12} \text{ nm}}{1 \text{ km}} 1 km1012 nm​.We put nanometers on top because that's what we want to end up with!

STEP 6

Alright, let's **multiply** our initial value by our conversion factor: 6×10−1 km⋅1012 nm1 km 6 \times 10^{-1} \text{ km} \cdot \frac{10^{12} \text{ nm}}{1 \text{ km}} 6×10−1 km⋅1 km1012 nm​

STEP 7

Notice how the **km units divide to one**, leaving us with just nanometers.Awesome! Now we just have: 6×10−1⋅1012 nm 6 \times 10^{-1} \cdot 10^{12} \text{ nm} 6×10−1⋅1012 nm

STEP 8

Let's **combine those exponents**: −1+12=11-1 + 12 = 11−1+12=11. 6×1011 nm 6 \times 10^{11} \text{ nm} 6×1011 nm

STEP 9

1. **12**2. 1012 nm1 km \frac{10^{12} \text{ nm}}{1 \text{ km}} 1 km1012 nm​3. 6×1011 nm 6 \times 10^{11} \text{ nm} 6×1011 nm

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to figure out how many nanometers are in $6 \times 10^{-1}$ kilometers! Watch out! Prefixes can be tricky!
Double-check those exponents, they can easily trip you up.

1. Magnitude Difference
2. Conversion Factor
3. Calculate Nanometers

We're going from kilometers to nanometers.
Remember, kilo means $10^3$ and nano means $10^{-9}$ .

To find the magnitude difference, we're looking at the difference between 3 and -9.
That's $3 - (-9) = 3 + 9 = \mathbf{12}$ .
So, there's a 12 order of magnitude difference between kilo and nano.

Since 1 kilometer is the same as $10^{12}$ nanometers, our conversion factor is $\frac{10^{12} \text{ nm}}{1 \text{ km}}$ .
We put nanometers on top because that's what we want to end up with!

Alright, let's multiply our initial value by our conversion factor: $6 \times 10^{-1} \text{ km} \cdot \frac{10^{12} \text{ nm}}{1 \text{ km}}$

Notice how the km units divide to one, leaving us with just nanometers.
Awesome! Now we just have: $6 \times 10^{-1} \cdot 10^{12} \text{ nm}$

Let's combine those exponents: $-1 + 12 = 11$ . $6 \times 10^{11} \text{ nm}$

1. 12
2. $\frac{10^{12} \text{ nm}}{1 \text{ km}}$
3. $6 \times 10^{11} \text{ nm}$