part b: short answer (1 mark each – total: 4 marks)
6. write the number 7020 in scientific notation, using 3 significant digits.
answer: _______________
7. round 9.8765 × 10⁷ to 3 significant digits.
answer: _______________
8. how many significant digits are in the measurement 6.070 × 10⁻⁴?
answer: _______________
9. a student records the following measurement: 0.004070 kg. how many significant digits does this number have?
answer: _______________

part c: calculations (2 marks each – total: 8 marks)
perform the operations and round your answer based on the correct number of significant digits.
10. multiply:
(3.25 m) × (2.1 m) = _______________
11. add:
(12.11 g) + (0.034 g) + (0.2 g) = _______________
12. subtract:
(105.6 ml) − (35.25 ml) = _______________
13. divide:
(8.400 m) ÷ (2.0 s) = _______________

Question

part b: short answer (1 mark each – total: 4 marks)
6. write the number 7020 in scientific notation, using 3 significant digits.
answer: _______________
7. round 9.8765 × 10⁷ to 3 significant digits.
answer: _______________
8. how many significant digits are in the measurement 6.070 × 10⁻⁴?
answer: _______________
9. a student records the following measurement: 0.004070 kg. how many significant digits does this number have?
answer: _______________

part c: calculations (2 marks each – total: 8 marks)
perform the operations and round your answer based on the correct number of significant digits.
10. multiply:
(3.25 m) × (2.1 m) = _______________
11. add:
(12.11 g) + (0.034 g) + (0.2 g) = _______________
12. subtract:
(105.6 ml) − (35.25 ml) = _______________
13. divide:
(8.400 m) ÷ (2.0 s) = _______________

Accepted Answer

### Question 6
# Explanation:
## Step1: Identify significant digits
7020 has digits 7, 0, 2, 0. The first three significant digits are 7, 0, 2 (note that leading zeros don't count, but zeros between non - zero digits do).
## Step2: Express in scientific notation
To write in scientific notation, we move the decimal point so that there is one non - zero digit to the left of the decimal. For 7020, we can write it as $7.02\times10^{3}$ (since $7.02\times10^{3}=7.02\times1000 = 7020$)
# Answer: $7.02\times10^{3}$

### Question 7
# Explanation:
## Step1: Identify the first three significant digits
For the number $9.8765\times 10^{7}$, the significant digits are 9, 8, 7, 6, 5. The first three are 9, 8, 7.
## Step2: Round the fourth digit
The fourth digit is 6, which is greater than 5. So we round up the third digit. $9.8765\approx9.88$ when rounded to three significant digits.
## Step3: Write the number in scientific notation
So $9.8765\times 10^{7}\approx9.88\times 10^{7}$
# Answer: $9.88\times 10^{7}$

### Question 8
# Explanation:
In the number $6.070\times 10^{-4}$, the significant digits are determined by the coefficient. The digits in the coefficient 6.070 are 6, 0, 7, 0. All non - zero digits and zeros between non - zero digits and trailing zeros in a decimal number are significant. So there are 4 significant digits.
# Answer: 4

### Question 9
# Explanation:
For the number 0.004070 kg, leading zeros (the three zeros before 4) are not significant. The non - zero digit 4, the zero between 4 and 7, the 7, and the trailing zero are significant. So the significant digits are 4, 0, 7, 0. So there are 4 significant digits.
# Answer: 4

### Question 10
# Explanation:
## Step1: Multiply the numbers
$(3.25\ m)\times(2.1\ m)=3.25\times2.1\ m^{2}$
$3.25\times2.1 = 6.825$
## Step2: Determine significant digits
3.25 has 3 significant digits and 2.1 has 2 significant digits. When multiplying, the result should have the same number of significant digits as the number with the least number of significant digits. So we round to 2 significant digits? Wait, no: 3.25 has 3, 2.1 has 2. The rule for multiplication/division is that the result has the same number of significant digits as the factor with the fewest significant digits. So 2.1 has 2 significant digits? Wait, no, 2.1 has two significant digits? Wait, 3.25 has three, 2.1 has two. Wait, no, 2.1: the non - zero digits are 2 and 1, so two significant digits? Wait, no, 2.1 is two significant digits? Wait, 3.25 is three, 2.1 is two. So the product should have two significant digits? Wait, no, 3.25×2.1: 3.25 has three, 2.1 has two. The number of significant digits in the result is determined by the least number, which is two? Wait, no, 2.1 has two significant digits? Wait, 2.1: the digit 2 and 1, so two. But 3.25×2.1 = 6.825. Rounding to two significant digits: 6.8 (wait, no, 6.825 rounded to two significant digits is 6.8? Wait, no, 6.825: the first two significant digits are 6 and 8. The next digit is 2, which is less than 5, so we keep it as 6.8? Wait, no, 3.25 has three, 2.1 has two. Wait, maybe I made a mistake. 2.1 has two significant digits, 3.25 has three. So the result should have two significant digits. Wait, 3.25×2.1 = 6.825. Rounding to two significant digits: 6.8? Wait, no, 6.825 rounded to two significant digits is 6.8? Wait, no, 6.825: the first significant digit is 6, the second is 8, the third is 2. Since we need two, we look at the third digit to round. 2 < 5, so we keep 6.8. But wait, 3.25 is three sig figs, 2.1 is two. The rule is that the number of sig figs in the result is equal to the number of sig figs in the least precise measurement. So 2.1 has two, so the answer should have two. But wait, 3.25×2.1 = 6.825. If we consider 2.1 as two sig figs and 3.25 as three, the product should have two sig figs. So 6.8 $m^{2}$? Wait, no, 3.25 has three, 2.1 has two. Wait, maybe I messed up. Let's recalculate 3.25×2.1: 3×2.1 = 6.3, 0.25×2.1 = 0.525, so total is 6.3 + 0.525 = 6.825. Now, 3.25 has three significant digits, 2.1 has two. The rule for multiplication is that the result has the same number of significant digits as the factor with the least number of significant digits. So 2.1 has two, so we round 6.825 to two significant digits. 6.825 rounded to two significant digits: look at the third digit (2), which is less than 5, so we keep the second digit as it is. So 6.8 $m^{2}$? Wait, but 6.825 is closer to 6.8 than 6.9? Wait, no, 6.825: the first two digits are 6 and 8, the third is 2. So when rounding to two significant digits, we have 6.8. But wait, some sources say that when multiplying, the number of significant digits is determined by the smallest number of significant digits in the factors. So 3.25 (3 sig figs) × 2.1 (2 sig figs) = 6.8 (2 sig figs).
# Answer: $6.8\ m^{2}$

### Question 11
# Explanation:
## Step1: Add the numbers
$(12.11\ g)+(0.034\ g)+(0.2\ g)=12.11 + 0.034+0.2$
$12.11+0.034 = 12.144$
$12.144 + 0.2=12.344$
## Step2: Determine significant digits for addition
When adding, we look at the decimal places. 12.11 has two decimal places, 0.034 has three, 0.2 has one. The number with the least number of decimal places is 0.2 (one decimal place). So we round the sum to one decimal place. 12.344 rounded to one decimal place is 12.3.
# Answer: $12.3\ g$

### Question 12
# Explanation:
## Step1: Subtract the numbers
$(105.6\ mL)-(35.25\ mL)=105.6 - 35.25=70.35$
## Step2: Determine significant digits for subtraction
105.6 has one decimal place, 35.25 has two decimal places. We round to one decimal place (since 105.6 has the least number of decimal places). 70.35 rounded to one decimal place is 70.4.
# Answer: $70.4\ mL$

### Question 13
# Explanation:
## Step1: Divide the numbers
$(8.400\ m)\div(2.0\ s)=\frac{8.400}{2.0}\ m/s$
$8.400\div2.0 = 4.2$ (wait, 8.400 has four significant digits, 2.0 has two. When dividing, the result should have two significant digits? Wait, 8.400÷2.0: 8.400 has four, 2.0 has two. So the result should have two significant digits. 8.400÷2.0 = 4.2 (exactly, but 2.0 has two sig figs, 8.400 has four. So 4.2 has two sig figs? Wait, 8.400÷2.0 = 4.200? No, 8.400÷2.0: 2.0 is two sig figs, so the answer should be two sig figs. 8.400÷2.0 = 4.2 (since 8.4÷2.0 = 4.2). Wait, 8.400 has four sig figs, 2.0 has two. So the quotient should have two sig figs. So 4.2 $m/s$.
# Answer: $4.2\ m/s$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 6

Step1: Identify significant digits

Step2: Express in scientific notation

Step1: Identify the first three significant digits

Step2: Round the fourth digit

Step3: Write the number in scientific notation

Answer:

Question 7