Question

scientific notation and the metric conversions
date
put the correct answer for each question in the blank provided.
1 convert 52000 to scientific notation.
a $5.2×10^4$ b $5.2×10^{-4}$ c $52×10^{-4}$ d $52×10^4$
2 convert 0.0012 to scientific notation.
a $12×10^3$ b $12×10^{-3}$ c $1.2×10^{-3}$ d $1.2×10^3$
3 $(7.2×10^6)+(2.3×10^6)$
a $9.5×10^6$ b $9.5×10^6$ c $95×10$ d $9.6×10^6$
4 $(2.0×10^7)×(3.0×10^4)$
a $6.0×10^4$ b $5.0×10^4$ c $6.0×10^{16}$ d $6.0×10^9$
5 convert 23 centimeters (cm) into meters (m).
a 230 m b 2.3 m c 0.23 m d 0.023 m
6 convert 6 meters (m) into millimeters (mm).
a 0.6 mm b 60 mm c 600 mm d 6000 mm
show your work:
7 convert 5.6 kilograms to grams
8 convert 2.46 kilometers to meters.

Explanation:

Step1: Convert 52000 to scientific notation

Scientific notation requires a number between 1-10 times a power of 10. $52000 = 5.2 \times 10^4$

Step2: Convert 0.0012 to scientific notation

Move decimal to get 1.2, count 3 left moves: $0.0012 = 1.2 \times 10^{-3}$

Step3: Add $(7.2 \times 10^4)+(2.3 \times 10^4)$

Factor out $10^4$: $(7.2+2.3) \times 10^4 = 9.5 \times 10^4$

Step4: Multiply $(2.0 \times 10^7) \times (3.0 \times 10^4)$

Multiply coefficients, add exponents: $(2.0 \times 3.0) \times 10^{7+4} = 6.0 \times 10^{11}$

Step5: Convert 23 cm to meters

1 m = 100 cm, so $23 \times \frac{1}{100} = 0.23$ m

Step6: Convert 6 m to millimeters

1 m = 1000 mm, so $6 \times 1000 = 6000$ mm

Step7: Convert 5.6 kg to grams

1 kg = 1000 g, so $5.6 \times 1000 = 5600$ g

Step8: Convert 2.46 km to meters

1 km = 1000 m, so $2.46 \times 1000 = 2460$ m

Answer:

1. A. $5.2 \times 10^4$
2. C. $1.2 \times 10^{-3}$
3. A. $9.5 \times 10^4$
4. C. $6.0 \times 10^{11}$
5. C. 0.23 m
6. D. 6000 mm
7. 5600 grams
8. 2460 meters