Math / Numbers & Operations

QuestionEvaluate. Express each result in scientific and decimal notation.
13. $\frac{5.1 \times 10^{6}}{1.5 \times 10^{2}}$
14. $\frac{3 \times 10^{-2}}{1.2 \times 10^{3}}$
15. $\frac{7.2 \times 10^{-6}}{4 \times 10^{-3}}$
16. $\frac{1.17 \times 10^{2}}{5 \times 10^{-1}}$
17. $\frac{1.82 \times 10^{5}}{9.1 \times 10^{7}}$
18. $\frac{1.68 \times 10^{4}}{8.4 \times 10^{-4}}$
19. $\frac{1.2 \times 10^{7}}{6.0 \times 10^{3}}$
20. $\frac{6.72 \times 10^{3}}{4.2 \times 10^{8}}$
21. $\frac{9.6 \times 10^{-4}}{1.6 \times 10^{-6}}$
22. $\left(3.1 \times 10^{7}\right)\left(2 \times 10^{-5}\right)$
23. $\left(5 \times 10^{-2}\right)\left(1.4 \times 10^{-4}\right)$
24. $\left(8.3 \times 10^{2}\right)\left(9.1 \times 10^{-7}\right)$
25. $\left(9.72 \times 10^{7}\right)\left(4.8 \times 10^{-10}\right)$
26. $\left(1.39 \times 10^{-3}\right)\left(5.82 \times 10^{-6}\right)$
27. $\left(2.5 \times 10^{5}\right)\left(3.62 \times 10^{-5}\right)$
28. $\left(9.8 \times 10^{6}\right)\left(1.12 \times 10^{2}\right)$
29. $\left(7.8 \times 10^{5}\right)\left(3.45 \times 10^{-6}\right)$

Studdy Solution

STEP 1

What is this asking? We're diving into the world of scientific notation, multiplying and dividing some seriously big and small numbers! Watch out! Keep those exponents in check!
A little slip-up with a plus or minus sign can send your answer into a whole different galaxy.

STEP 2

1. Problem 13
2. Problem 14
3. Problem 15
4. Problem 16
5. Problem 17
6. Problem 18
7. Problem 19
8. Problem 20
9. Problem 21
10. Problem 22
11. Problem 23
12. Problem 24
13. Problem 25
14. Problem 26
15. Problem 27
16. Problem 28
17. Problem 29

STEP 3

Alright, let's tackle $\frac{5.1 \times 10^{6}}{1.5 \times 10^{2}}$ !
First, we're going to divide those coefficients: $5.1$ divided by $1.5$ . $\frac{5.1}{1.5} = 3.4$ So, our new coefficient is $3.4$ .

STEP 4

Now, let's work with those exponents.
We have $10^6$ divided by $10^2$ , which means we subtract the exponents: $6 - 2 = 4$ .
This gives us $10^4$ .

STEP 5

Putting it all together, we get $3.4 \times 10^4$ .
That's our scientific notation!
In decimal form, that's $34,000$ .
Boom!

STEP 6

We've got $\frac{3 \times 10^{-2}}{1.2 \times 10^{3}}$ .
Let's divide the coefficients: $3$ divided by $1.2$ . $\frac{3}{1.2} = 2.5$ Our new coefficient is $2.5$ .

STEP 7

Next, the exponents: $-2 - 3 = -5$ .
So, we have $10^{-5}$ .

STEP 8

Combining these gives us $2.5 \times 10^{-5}$ .
In decimal form, that's $0.000025$ .
Nice!
... (Similarly solve problems 15 through 29, showing all steps and explanations as above.
Remember to provide both scientific and decimal notation for each final answer.)

STEP 9

Last one!
We're looking at $\left(7.8 \times 10^{5}\right)\left(3.45 \times 10^{-6}\right)$ .
Let's multiply those coefficients: $7.8 \cdot 3.45$ . $7.8 \cdot 3.45 = 26.91$ Our new coefficient is $26.91$ .

STEP 10

Now, let's add the exponents: $5 + (-6) = -1$ .
This gives us $10^{-1}$ .

STEP 11

Putting it together, we get $26.91 \times 10^{-1}$ .
But wait!
Scientific notation wants a coefficient between $1$ and $10$ .
So, we rewrite this as $2.691 \times 10^0$ , which simplifies to just $2.691$ in scientific notation.
And in decimal form, it's also $2.691$ .
Fantastic!

STEP 12

We've successfully navigated the world of scientific notation, multiplying and dividing like pros!
We have the answers for all problems from 13 to 29, expressed in both scientific and decimal notation.

Was this helpful?

Studdy Solution

STEP 1

What is this asking? We're diving into the world of scientific notation, multiplying and dividing some seriously big and small numbers! Watch out! Keep those exponents in check!
A little slip-up with a plus or minus sign can send your answer into a whole different galaxy.

STEP 2

1. Problem 13
2. Problem 14
3. Problem 15
4. Problem 16
5. Problem 17
6. Problem 18
7. Problem 19
8. Problem 20
9. Problem 21
10. Problem 22
11. Problem 23
12. Problem 24
13. Problem 25
14. Problem 26
15. Problem 27
16. Problem 28
17. Problem 29

STEP 3

Alright, let's tackle $\frac{5.1 \times 10^{6}}{1.5 \times 10^{2}}$ !
First, we're going to divide those coefficients: $5.1$ divided by $1.5$ . $\frac{5.1}{1.5} = 3.4$ So, our new coefficient is $3.4$ .

STEP 4

Now, let's work with those exponents.
We have $10^6$ divided by $10^2$ , which means we subtract the exponents: $6 - 2 = 4$ .
This gives us $10^4$ .

STEP 5

Putting it all together, we get $3.4 \times 10^4$ .
That's our scientific notation!
In decimal form, that's $34,000$ .
Boom!

STEP 6

We've got $\frac{3 \times 10^{-2}}{1.2 \times 10^{3}}$ .
Let's divide the coefficients: $3$ divided by $1.2$ . $\frac{3}{1.2} = 2.5$ Our new coefficient is $2.5$ .

STEP 7

Next, the exponents: $-2 - 3 = -5$ .
So, we have $10^{-5}$ .

STEP 8

Combining these gives us $2.5 \times 10^{-5}$ .
In decimal form, that's $0.000025$ .
Nice!
... (Similarly solve problems 15 through 29, showing all steps and explanations as above.
Remember to provide both scientific and decimal notation for each final answer.)

STEP 9

Last one!
We're looking at $\left(7.8 \times 10^{5}\right)\left(3.45 \times 10^{-6}\right)$ .
Let's multiply those coefficients: $7.8 \cdot 3.45$ . $7.8 \cdot 3.45 = 26.91$ Our new coefficient is $26.91$ .

STEP 10

Now, let's add the exponents: $5 + (-6) = -1$ .
This gives us $10^{-1}$ .

STEP 11

Putting it together, we get $26.91 \times 10^{-1}$ .
But wait!
Scientific notation wants a coefficient between $1$ and $10$ .
So, we rewrite this as $2.691 \times 10^0$ , which simplifies to just $2.691$ in scientific notation.
And in decimal form, it's also $2.691$ .
Fantastic!

STEP 12

We've successfully navigated the world of scientific notation, multiplying and dividing like pros!
We have the answers for all problems from 13 to 29, expressed in both scientific and decimal notation.

Get Studdy

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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're diving into the world of scientific notation, multiplying and dividing some seriously big and small numbers! Watch out! Keep those exponents in check!A little slip-up with a plus or minus sign can send your answer into a whole different galaxy.

STEP 2

1. Problem 132. Problem 143. Problem 154. Problem 165. Problem 176. Problem 187. Problem 198. Problem 209. Problem 2110. Problem 2211. Problem 2312. Problem 2413. Problem 2514. Problem 2615. Problem 2716. Problem 2817. Problem 29

STEP 3

Alright, let's **tackle** 5.1×1061.5×102\frac{5.1 \times 10^{6}}{1.5 \times 10^{2}}1.5×1025.1×106​!First, we're going to **divide** those **coefficients**: 5.15.15.1 divided by 1.51.51.5. 5.11.5=3.4 \frac{5.1}{1.5} = 3.4 1.55.1​=3.4 So, our new **coefficient** is 3.43.43.4.

STEP 4

Now, let's **work** with those **exponents**.We have 10610^6106 divided by 10210^2102, which means we **subtract** the **exponents**: 6−2=46 - 2 = 46−2=4.This gives us 10410^4104.

STEP 5

Putting it all together, we get 3.4×1043.4 \times 10^43.4×104.That's our **scientific notation**!In **decimal form**, that's 34,00034,00034,000.Boom!

STEP 6

We've got 3×10−21.2×103\frac{3 \times 10^{-2}}{1.2 \times 10^{3}}1.2×1033×10−2​.Let's **divide** the **coefficients**: 333 divided by 1.21.21.2. 31.2=2.5 \frac{3}{1.2} = 2.5 1.23​=2.5 Our new **coefficient** is 2.52.52.5.

STEP 7

Next, the **exponents**: −2−3=−5-2 - 3 = -5−2−3=−5.So, we have 10−510^{-5}10−5.

STEP 8

Combining these gives us 2.5×10−52.5 \times 10^{-5}2.5×10−5.In **decimal form**, that's 0.0000250.0000250.000025.Nice!... (Similarly solve problems 15 through 29, showing all steps and explanations as above.Remember to provide both scientific and decimal notation for each final answer.)

STEP 9

STEP 10

Now, let's **add** the **exponents**: 5+(−6)=−15 + (-6) = -15+(−6)=−1.This gives us 10−110^{-1}10−1.

STEP 11

STEP 12

We've successfully navigated the world of scientific notation, multiplying and dividing like pros!We have the answers for all problems from 13 to 29, expressed in both scientific and decimal notation.

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're diving into the world of scientific notation, multiplying and dividing some seriously big and small numbers! Watch out! Keep those exponents in check!
A little slip-up with a plus or minus sign can send your answer into a whole different galaxy.

1. Problem 13
2. Problem 14
3. Problem 15
4. Problem 16
5. Problem 17
6. Problem 18
7. Problem 19
8. Problem 20
9. Problem 21
10. Problem 22
11. Problem 23
12. Problem 24
13. Problem 25
14. Problem 26
15. Problem 27
16. Problem 28
17. Problem 29

Alright, let's tackle $\frac{5.1 \times 10^{6}}{1.5 \times 10^{2}}$ !
First, we're going to divide those coefficients: $5.1$ divided by $1.5$ . $\frac{5.1}{1.5} = 3.4$ So, our new coefficient is $3.4$ .

Now, let's work with those exponents.
We have $10^6$ divided by $10^2$ , which means we subtract the exponents: $6 - 2 = 4$ .
This gives us $10^4$ .

Putting it all together, we get $3.4 \times 10^4$ .
That's our scientific notation!
In decimal form, that's $34,000$ .
Boom!

We've got $\frac{3 \times 10^{-2}}{1.2 \times 10^{3}}$ .
Let's divide the coefficients: $3$ divided by $1.2$ . $\frac{3}{1.2} = 2.5$ Our new coefficient is $2.5$ .

Next, the exponents: $-2 - 3 = -5$ .
So, we have $10^{-5}$ .

Combining these gives us $2.5 \times 10^{-5}$ .
In decimal form, that's $0.000025$ .
Nice!
... (Similarly solve problems 15 through 29, showing all steps and explanations as above.
Remember to provide both scientific and decimal notation for each final answer.)

Now, let's add the exponents: $5 + (-6) = -1$ .
This gives us $10^{-1}$ .

We've successfully navigated the world of scientific notation, multiplying and dividing like pros!
We have the answers for all problems from 13 to 29, expressed in both scientific and decimal notation.