Question

physical science 1st semester exam multiple choice: circle the letter. 1) there are ____ meters in a megameter. a) 1,000 b) 10,000 c) 100,000 d) 1,000,000 2) if you convert 0.84642 dm to nm, your answer would be ____ nm a) 8464.2 b) 84,642,000 c) 0.000846412 d) 0.0000000

Explanation:

Question 1

Step1: Recall metric prefixes

Mega- ($M$) is a metric prefix representing $10^6$ (1,000,000). So 1 megameter ($Mm$) = $10^6$ meters.

Step2: Match with options

We need to find how many meters are in a megameter. Since $1\ Mm = 10^6\ m = 1,000,000\ m$, the correct option is d.

Step1: Recall unit conversions

1 decimeter ($dm$) = $0.1\ m$ = $10^{-1}\ m$, 1 nanometer ($nm$) = $10^{-9}\ m$. First, convert $dm$ to $m$: $0.84642\ dm = 0.84642\times10^{-1}\ m = 8.4642\times10^{-2}\ m$.

Step2: Convert $m$ to $nm$

Since $1\ m = 10^9\ nm$, multiply the value in meters by $10^9$: $8.4642\times10^{-2}\ m\times10^9\ nm/m = 8.4642\times10^{7}\ nm = 84642000\ nm$? Wait, no, wait the options: Wait, let's re - calculate. Wait, $0.84642\ dm$: 1 dm = 10 cm, 1 cm = 10 mm, 1 mm = 1000 μm, 1 μm = 1000 nm. So 1 dm = $10\times10\times1000\times1000\ nm=10^8\ nm$. So $0.84642\ dm = 0.84642\times10^8\ nm = 84642000\ nm$? But the options: Wait the options are a) 8464.2, b) 84,642,000, c) 0.000846412, d) 0.000000084642. Wait, maybe I made a mistake in the conversion factor. Wait, 1 dm = 0.1 m, 1 m = $10^9$ nm, so 1 dm = $0.1\times10^9\ nm = 10^8\ nm$. So $0.84642\ dm=0.84642\times10^8\ nm = 84642000\ nm$? But the options have b) 84,642,000. Wait, maybe the original number is 0.084642 dm? Wait, the problem says "0.84642 dm". Wait, let's check the options again. Wait, option b is 84,642,000. Wait, maybe I miscalculated. Wait, 1 dm = 10 cm, 1 cm = 10 mm, 1 mm = 1000 μm, 1 μm = 1000 nm. So 1 dm = $10\times10\times1000\times1000\ nm = 10^8\ nm$. So $0.84642\ dm=0.84642\times10^8\ nm = 84642000\ nm$, which is 84,642,000 nm. So the correct option is b.

Answer:

d. 1,000,000

Question 2