12. the number of significant figures in the measured value 0.00320 g is
a. 2.
b. 3.
c. 5.
d. 6.
13. the number of significant figures in the measurement 170.040 km is
a. 3.
b. 4.
c. 5.
d. 6.
14. the number that has five significant figures is
a. 23,410
b. 0.00652
c. 0.01783
d. 10.292
15. the dimensions of a rectangular solid are measured to be 1.27 cm, 1.3 cm, and 2.5 cm. the volume should be recorded as
a. 4.128 cm³.
b. 4.12 cm³.
c. 4.13 cm³.
d. 4.1 cm³.
16. three samples of 0.12 g, 1.8 g, and 0.562 g are mixed together. the combined mass of all three samples, expressed to the correct number of significant figures, should be recorded as
a. 2.4 g.
b. 2.48 g.
c. 2.482 g.
d. 2.5 g.
17. round 1.245633501 × 10⁸ to four significant figures.
a. 1246
b. 1.2456 × 10⁸
c. 1.246 × 10⁸
d. 1.246 × 10⁴
18. the measurement 0.035550 g rounded off to two significant figures would be
a. 0.03 g.
b. 0.35 g.
c. 0.036 g.
d. 3.5 × 10⁻² g.
19. written in scientific notation, the measurement 0.000065 cm is
a. 65 × 10⁻⁴ cm.
b. 6.5 × 10⁻⁵ cm.
c. 6.5 × 10⁻⁶ cm.
d. 6.5 × 10⁻⁴ cm.
20. the speed of light is 300,000 km/s. in scientific notation, this speed is
a. 3 × 10⁵ km/s.
b. 3.00 × 10⁵ km/s.
c. 3.0 × 10⁶ km/s.
d. 3.00 × 10⁶ km/s.
21. the expression of 5008 km in scientific notation is ____.
a. 5.008 × 10³ km
b. 50.08 × 10⁻⁴ km
c. 5.008 × 10⁻³ km
d. 5.008 × 10⁴ km
22. what is 78,900,000,000 expressed in scientific notation?
a. 789 × 10⁹
b. 78.9 × 10⁸
c. 7.89 × 10⁹
d. 7.89 × 10¹⁰

Question

Accepted Answer

### Question 12
# Answer:
b. 3
# Explanation:
## Step1: Recall significant figure rules
Leading zeros are not significant. Non - zero digits and trailing zeros after a non - zero digit in a decimal number are significant.
## Step2: Analyze 0.00320
The leading zeros (0.00) are not significant. The non - zero digit 3, the digit 2, and the trailing zero after 2 (because it is after a non - zero digit in a decimal) are significant. So there are 3 significant figures.

### Question 13
# Answer:
d. 6
# Explanation:
## Step1: Recall significant figure rules
All non - zero digits, zeros between non - zero digits, and trailing zeros after a decimal are significant.
## Step2: Analyze 170.040
The digits 1, 7, 0 (between 7 and 0), 0 (after decimal), 4, 0 (trailing after 4) are all significant. So 1 (1) + 1 (7)+1 (0)+1 (0)+1 (4)+1 (0) = 6 significant figures.

### Question 14
# Answer:
d. 10.292
# Explanation:
## Step1: Recall significant figure rules
- For option a (23,410): The trailing zero may or may not be significant (it could be a placeholder), so it has 4 or 5 significant figures (ambiguous).
- For option b (0.00652): Leading zeros are not significant, so it has 3 significant figures.
- For option c (0.01783): Leading zeros are not significant, so it has 4 significant figures.
- For option d (10.292): All the digits 1, 0, 2, 9, 2 are significant (the zero is between non - zero digits), so it has 5 significant figures.

### Question 15
# Answer:
d. $4.1\space cm^{3}$
# Explanation:
## Step1: Recall significant figure rules for multiplication
When multiplying, the result should have the same number of significant figures as the number with the least number of significant figures in the multiplication.
## Step2: Analyze the dimensions
The dimensions are $1.27\space cm$ (3 significant figures), $1.3\space cm$ (2 significant figures), and $2.5\space cm$ (2 significant figures). The least number of significant figures is 2.
## Step3: Calculate the volume
Volume $V=1.27\times1.3\times2.5 = 4.1225\space cm^{3}$. Rounding to 2 significant figures gives $4.1\space cm^{3}$.

### Question 16
# Answer:
d. 2.5 g
# Explanation:
## Step1: Recall significant figure rules for addition
When adding, the result should be rounded to the least precise decimal place (the least number of decimal places in the numbers being added).
## Step2: Add the masses
$0.12 + 1.8+0.562=2.482\space g$. The number $1.8$ has one decimal place, which is the least number of decimal places.
## Step3: Round the result
Rounding $2.482$ to one decimal place gives $2.5\space g$.

### Question 17
# Answer:
c. $1.246\times10^{8}$
# Explanation:
## Step1: Recall significant figure rules for rounding
To round to four significant figures, we look at the fifth significant figure.
## Step2: Analyze $1.245633501\times10^{8}$
The first four significant figures are 1, 2, 4, 5. The fifth significant figure is 6. Since 6 > 5, we round up the fourth significant figure. So $1.245633501\times10^{8}\approx1.246\times10^{8}$ when rounded to four significant figures.

### Question 18
# Answer:
c. 0.036 g
# Explanation:
## Step1: Recall significant figure rules for rounding
We want two significant figures. The first non - zero digit is 3 (first significant figure), the next digit is 5 (second significant figure candidate), and the digit after 5 is 5.
## Step2: Round the number
$0.035550$ g. The first significant figure is 3, the second is 5. The digit after 5 is 5, so we round up the 5 to 6. So $0.035550\space g\approx0.036\space g$ when rounded to two significant figures.

### Question 19
# Answer:
b. $6.5\times10^{- 5}\space cm$
# Explanation:
## Step1: Recall scientific notation rules
Scientific notation is of the form $a\times10^{n}$, where $1\leqslant|a|\lt10$ and $n$ is an integer.
## Step2: Convert 0.000065 to scientific notation
We move the decimal point 5 places to the right to get $a = 6.5$ and $n=- 5$. So $0.000065\space cm = 6.5\times10^{-5}\space cm$.

### Question 20
# Answer:
b. $3.00\times10^{5}\space km/s$
# Explanation:
## Step1: Recall scientific notation rules
The speed of light is $300000\space km/s$. To express it in scientific notation with proper significant figures (if we consider that 300000 may have 3 significant figures as $3.00\times10^{5}$).
## Step2: Analyze the options
- Option a: $3\times10^{5}$ has 1 significant figure.
- Option b: $3.00\times10^{5}$ has 3 significant figures, which is appropriate if we consider the precision.
- Option c: $3.0\times10^{6}$ is incorrect (magnitude is wrong).
- Option d: $3.00\times10^{6}$ is incorrect (magnitude is wrong).

### Question 21
# Answer:
a. $5.008\times10^{3}\space km$
# Explanation:
## Step1: Recall scientific notation rules
We need to express $5008$ in the form $a\times10^{n}$ where $1\leqslant|a|\lt10$.
## Step2: Convert 5008 to scientific notation
Move the decimal point 3 places to the left to get $a = 5.008$ and $n = 3$. So $5008\space km=5.008\times10^{3}\space km$.

### Question 22
# Answer:
d. $7.89\times10^{10}$
# Explanation:
## Step1: Recall scientific notation rules
We need to express $78900000000$ in the form $a\times10^{n}$ where $1\leqslant|a|\lt10$.
## Step2: Convert 78900000000 to scientific notation
Move the decimal point 10 places to the left to get $a = 7.89$ and $n = 10$. So $78900000000=7.89\times10^{10}$.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 12

Step1: Recall significant figure rules

Step2: Analyze 0.00320

Question 13

Step1: Recall significant figure rules

Step2: Analyze 170.040

Question 14

Step1: Recall significant figure rules

Question 15

Answer: