Numbers in Scientific Calculations
Write 0.00052 in scientific notation
5.2 × 10⁻⁴
1 km = ? m
1000m
True/False → “Zeros at the end of a number without a decimal point are significant.”
False. (Trailing zeros without a decimal are ambiguous unless notation clarifies.)
Set up the conversion: 2.5 hours → minutes.
2.5 hr × (60 min / 1 hr) = 150 min.
If a pen weighs 0.012 kg, how many grams is that?
12.0 g. (0.012 kg × 1000 = 12)
7.25 × 10⁵ in standard form
725000.
Convert 5600 m to km.
5.6 km
How many sig figs in 0.000340?
3 sf (digits: 3, 4, trailing 0 after decimal counts).
Convert 4.5 L → mL
4500 mL.
A runner completes 5.0 km in 25 minutes. What is their average speed in m/s?
Convert 5.0 km → 5000 m
time = 25 min = 1500 s
speed = 5000 / 1500 = 3.33 m/s
Round 45.6789 to 3 sig figs
45.7 (First 3 sig figs are 4,5,6; next digit is 7 → 6 rounds to 7.)
Convert 0.035 kg to g
0.035 × 1000 = 35
Add 24.56 + 3.0, with correct sig figs.
addition rule → least decimal places = 1
→ 24.56 + 3.0 = 27.56
→ round to 27.6.
Convert 25.0 g to kg.
0.0250 kg.
(25.0 g × 1 kg / 1000 g)
A block has a mass of 12.5 g and a volume of 4.1 cm³. What is its density?
12.5 / 4.1 = 3.05 g/cm³
3.0 g/cm³
3.25 × 10³ ÷ 6.5 × 10² with correct sig figs
(3250 ÷ 650) = 5.0
final to 2 sf → 5.0
Convert 2.5 × 10⁵ mm to km.
250000 mm = 250 m = 0.25 km.
Multiply 2.34 × 0.056, give answer with correct sig figs.
multiply then round to least sf (2 sf):
= 0.13104 → 0.13.
How many seconds are in 2.50 days? (full setup + answer)
2.50 d × 24 hr/d × 3600 s/hr = 216000 s
A solid metal cube has a mass of 2.35 kg and each side length is 5.00 cm.
Calculate the cube’s density in g/cm³.
Convert that density into kg/m³.
Convert mass: 2.35 kg × (1000 g / 1 kg) = 2350 g
Volume: (5.00 cm)³ = 125 cm³
Density = 2350 g ÷ 125 cm³ = 18.8 g/cm³ (3 sf)
Convert to kg/m³: 18.8 g/cm³ × (1000 kg / 1 g) × (1,000,000 cm³ / 1 m³)
= 1.88 × 10⁴ kg/m³
Final Answer: 18.8 g/cm³ and 1.88 × 10⁴ kg/m³
Calculator shows 1.23456789 × 10⁶. Round to 4 sig figs
1.235 × 10⁶
A car travels 95.0 km. Express this distance in meters and centimeters with correct sig figs.
Meters: 95.0 km = 95.0 × 1000 = 9.50 × 10⁴ m
Centimeters: 95.0 km = 9.50 × 10⁶ cm.
Why is the number 1000 written differently in scientific notation depending on sig figs? (Explain conceptually.)
Scientific notation explicitly shows significant figures. Example: 1000 (1 sf) = 1 × 10³; 1000. (4 sf) = 1.000 × 10³. The trailing zeros only count as significant if the notation (decimal or extra digits) indicates so.
Convert 65.0 miles to kilometers (1 mi = 1.609 km).
65.0 × 1.609 = 104.6 km (reporting to 3 sf as appropriate → 104.6 km).
A car travels 250. miles in 4.00 hours. Convert the speed into m/s with correct significant figures.
Distance = 250. miles × (1.609 km / 1 mile) = 402 km = 402000 m
Time = 4.00 hr × (3600 s / 1 hr) = 14400 s
Speed = 402000 ÷ 14400 = 27.9 m/s
Final Answer: 27.9 m/s (3 sig figs)