Significant Figures
**Task:** Answer questions on significant figures and scientific notation.
1. **What are significant figures?**
Options: A, B, C, D
Significant figures are the first non-zero digit and all digits that follow in a number.
Answer: C
2. **How many significant figures are in 0.00564?**
Leading zeros do not count.
Count digits: 5, 6, 4 → 3 significant figures.
Answer: B
3. **In 7.502, which digit is least significant?**
The least significant digit is the one farthest to the right: 2.
Answer: D
4. **Which number has 4 significant figures?**
A) 0.0120 → 3 digits (1,2,0)
B) 1200 → ambiguous but usually 2 unless specified
C) 0.00012 → 2 digits
D) 120.0 → counts trailing zero; 4 digits
Answer: D
5. **Convert 3.25 x 10^4 to standard form:**
Multiply: $3.25 \times 10^{4} = 32500$
Answer: C
6. **Significant figures in 700040?**
Without decimal point, trailing zeros ambiguous.
Here, likely 5 significant figures (7,0,0,0,4,0 → last zero ambiguous but if not decimal, omit last zero)
Assuming trailing zero significant, answer: C (5)
7. **Standard form of 5.6 x 10^-3:**
$5.6 \times 10^{-3} = 0.0056$
Answer: B
8. **Round 7.452 + 3.18 to 3 significant figures:**
Sum: $7.452 + 3.18 = 10.632$
Rounded to 3 significant figures: 10.6 (since 10.6 has 3 sig figs: 1,0,6)
Answer: A
9. **Convert 9.75 x 10^-2 to standard form:**
$9.75 \times 10^{-2} = 0.0975$
Answer: A
10. **Product of 2.3 x 10^3 and 1.5 x 10^-2:**
Multiply:
$$2.3 \times 10^{3} \times 1.5 \times 10^{-2} = 2.3 \times 1.5 \times 10^{3 + (-2)} = 3.45 \times 10^{1}$$
Standard form: $3.45 \times 10^{1} = 34.5$
Among options, match is 34.5 x 10^-3 (which is 0.0345, incorrect), 3.45 x 10^-5 (too small), 345 x 10^-4 ( = 0.0345), 3.45 x 10^4 (too large).
None matches exactly, but correct scientific notation is $3.45 \times 10^{1}$.
Given options discrepancy, closest is none strictly correct, but best matching standard form is 34.5 (needs no exponent).
So answer matches none exactly. Possibly misprint.
**Final answers:**
1:C
2:B
3:D
4:D
5:C
6:C
7:B
8:A
9:A
10: None exactly, exact is $3.45 \times 10^{1}$ (not among options)