16. a. what should you do to write ( 5.871 imes 10^{-7} ) in standard form?
b. express the number in standard form.
17. express ( 2.58 imes 10^{-2} ) in standard form.
18. at a certain point, the grand canyon is approximately 1,600,000 centimeters across.
a. express this number in scientific notation.
b. how many significant digits does the measurement have?
image of grand canyon with 1,600,000 cm
19. the length of a bacterial cell is ( 5.2 imes 10^{-6} ) meter. express the length of the cell in standard form.
20. higher order thinking express the distance 4,300,000 meters using scientific notation in meters, and then in millimeters.
21. which of the following numbers are written in scientific notation? select all that apply.
( 12 imes 10^6 )
12
( 6.89 imes 10^6 )
6.89
0.4
( 4 imes 10^{-1} )
22. jeana’s calculator display shows the number to the right.
image of calculator with 5.49 ee14
part a
express this number in scientific notation.
part b
express this number in standard form.
2-3 understand scientific notation

Question

16. a. what should you do to write ( 5.871 	imes 10^{-7} ) in standard form?
b. express the number in standard form.
17. express ( 2.58 	imes 10^{-2} ) in standard form.
18. at a certain point, the grand canyon is approximately 1,600,000 centimeters across.
a. express this number in scientific notation.
b. how many significant digits does the measurement have?
image of grand canyon with 1,600,000 cm
19. the length of a bacterial cell is ( 5.2 	imes 10^{-6} ) meter. express the length of the cell in standard form.
20. higher order thinking express the distance 4,300,000 meters using scientific notation in meters, and then in millimeters.
21. which of the following numbers are written in scientific notation? select all that apply.
( 12 	imes 10^6 )
12
( 6.89 	imes 10^6 )
6.89
0.4
( 4 	imes 10^{-1} )
22. jeana’s calculator display shows the number to the right.
image of calculator with 5.49 ee14
part a
express this number in scientific notation.
part b
express this number in standard form.
2-3 understand scientific notation

Accepted Answer

### Question 16a
# Explanation:
## Step1: Recall scientific to standard form
For a number in scientific notation $ a\times10^{n} $, if $ n $ is negative, we move the decimal point $ |n| $ places to the left. Here, $ 5.871\times10^{-7} $, $ n = - 7 $, so we move the decimal in 5.871 seven places to the left.
## Step2: Perform the movement
$ 5.871\times10^{-7}=0.0000005871 $ (we add leading zeros as needed: 5.871 → 0.5871 (1 place), 0.05871 (2), 0.005871 (3), 0.0005871 (4), 0.00005871 (5), 0.000005871 (6), 0.0000005871 (7)).
# Answer: Move the decimal point in 5.871 seven places to the left.

### Question 16b
# Explanation:
## Step1: Apply the rule from 16a
Using the same method as above, for $ 5.871\times10^{-7} $, move decimal 7 places left.
## Step2: Write the standard form
$ 5.871\times10^{-7}=0.0000005871 $
# Answer: $ 0.0000005871 $

### Question 17
# Explanation:
## Step1: Recall scientific to standard form
For $ 2.58\times10^{-2} $, $ n=-2 $, so move decimal 2 places left.
## Step2: Move the decimal
$ 2.58\times10^{-2}=0.0258 $ (2.58 → 0.258 (1 place), 0.0258 (2 places)).
# Answer: $ 0.0258 $

### Question 18a
# Explanation:
## Step1: Recall standard to scientific notation
Scientific notation is $ a\times10^{n} $, where $ 1\leq a < 10 $ and $ n $ is an integer. For 1,600,000, we move the decimal to get $ a = 1.6 $, and we moved 6 places, so $ n = 6 $.
## Step2: Write the scientific notation
$ 1,600,000 = 1.6\times10^{6} $
# Answer: $ 1.6\times10^{6} $

### Question 18b
# Explanation:
## Step1: Recall significant digits rules
Significant digits are the digits that carry meaning contributing to its precision. For 1,600,000 (or $ 1.6\times10^{6} $), the significant digits are 1 and 6 (since trailing zeros in a whole number without a decimal are not significant).
## Step2: Count the significant digits
So there are 2 significant digits.
# Answer: 2

### Question 19
# Explanation:
## Step1: Recall scientific to standard form
For $ 5.2\times10^{-6} $, $ n=-6 $, move decimal 6 places left.
## Step2: Move the decimal
$ 5.2\times10^{-6}=0.0000052 $ (5.2 → 0.52 (1), 0.052 (2), 0.0052 (3), 0.00052 (4), 0.000052 (5), 0.0000052 (6)).
# Answer: $ 0.0000052 $

### Question 20
# Explanation:
## Step1: Convert 4,300,000 to scientific notation (meters)
Move decimal to get $ a = 4.3 $, moved 6 places, so $ 4,300,000 = 4.3\times10^{6} $ meters.
## Step2: Convert meters to millimeters (1 meter = 1000 millimeters)
$ 4.3\times10^{6} $ meters $ = 4.3\times10^{6}\times10^{3} $ millimeters (since $ 1\mathrm{m}=10^{3}\mathrm{mm} $). Using exponent rule $ a^{m}\times a^{n}=a^{m + n} $, we get $ 4.3\times10^{6 + 3}=4.3\times10^{9} $ millimeters.
# Answer: In meters: $ 4.3\times10^{6} $ meters; In millimeters: $ 4.3\times10^{9} $ millimeters.

### Question 21
# Explanation:
## Step1: Recall scientific notation definition
Scientific notation is $ a\times10^{n} $, where $ 1\leq a < 10 $ and $ n $ is an integer.
- $ 12\times10^{6} $: $ a = 12$ (not between 1 and 10), so not scientific notation.
- $ 12 $: Not in scientific notation form.
- $ 6.89\times10^{6} $: $ a = 6.89 $ (1 ≤ 6.89 < 10), $ n = 6 $ (integer), so scientific notation.
- $ 6.89 $: Not in scientific notation form.
- $ 0.4 $: $ a = 0.4$ (less than 1), so not scientific notation.
- $ 4\times10^{-1} $: $ a = 4 $ (1 ≤ 4 < 10), $ n=-1 $ (integer), so scientific notation.
## Step2: Identify the correct ones
So $ 6.89\times10^{6} $ and $ 4\times10^{-1} $ are in scientific notation.
# Answer: $ 6.89\times10^{6} $, $ 4\times10^{-1} $

### Question 22 Part A
# Explanation:
## Step1: Recall calculator scientific notation
Calculator display "5.49 EE 14" means $ 5.49\times10^{14} $ (EE represents $ \times10^{\text{exponent}} $).
## Step2: Write the scientific notation
So the number in scientific notation is $ 5.49\times10^{14} $.
# Answer: $ 5.49\times10^{14} $

### Question 22 Part B
# Explanation:
## Step1: Recall scientific to standard form
For $ 5.49\times10^{14} $, $ n = 14 $, move decimal 14 places right.
## Step2: Move the decimal
$ 5.49\times10^{14}=549000000000000 $ (5.49 → 54.9 (1), 549 (2), then add 12 more zeros: 549000000000000).
# Answer: $ 549000000000000 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 16a

Step1: Recall scientific to standard form

Step2: Perform the movement

Step1: Apply the rule from 16a

Step2: Write the standard form

Step1: Recall scientific to standard form

Step2: Move the decimal

Answer:

Question 16b