NUMERICAL RESPONSE QUESTIONS

1. Write the following numbers in scientific notation:

a. 1234 m

• 1234= 1.234×10³ meters

b. 0.000023 s

• 0.000023=2.3×10⁻⁵

c. 469.3 × 10⁷ m

• 469.3×10⁷=4.693×10⁹ meters

d. 0.00985 × 10⁵ s

• 0.00985×10⁵=9.85×10¹ seconds

2. Express the following measurements using prefixes:

a. 27.5 × 10⁶ m

• 27.5×106 m=27.5 Mm (megameters)

b. 0.00023 × 10⁹ s

• 0.00023×109 s=230 ms (milliseconds)

3. If a boy is 15 years, 2 months, and 10 days old, convert his age into:

a. Seconds

• 1 year = 365 days (not accounting for leap years)
• 1 month = 30 days (approx.)
• 1 day = 24 hours = 86400 seconds

Total age in seconds:

• 15 years×365 days/year×86400 seconds/day
• 2 months×30 days/month×86400 seconds/day
• 10 days×86400 seconds/day

Total age in seconds:

• 473385600+5184000+864000=479019600 seconds

b. Milliseconds

• Since 1 second = 1000 milliseconds, multiply the seconds result by 1000.

Boy’s Age:

• 479019600×1000=479019600000 milliseconds

c. Megaseconds

• Since 1 megasecond = 10⁶ seconds, divide the total seconds by 10⁶

Boy’s age:

5. What is the pitch and least count of:

a. Vernier calipers

• Smallest division on the main scale = 1 mm = 0.1 cm
• Vernier scale has 20 divisions, so pitch = 1 mm/20=0.05 mm.

The least count = Pitch = 0.05 mm.

b. Screw gauge

• Smallest division on the main scale = 0.5 mm
• Movable scale has 50 divisions, so pitch = $\text{mm}$.

The least count = Pitch = 0.01 mm.