Question 1208239: A sugar ant is approximately 2 × 10^−3 meters long. If you put 10 million sugar
ants in a line, what is the distance from end to end?
200 meters
2,000 meters
20,000 meters
200,000 meters
Found 3 solutions by josgarithmetic, math_tutor2020, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source):
Answer by math_tutor2020(3816) (Show Source):
You can put this solution on YOUR website!
Answer: 20,000 meters
Work Shown
10 million = 10*(1 million)
= 10*10^6
= 10^1*10^6
= 10^(1+6)
= 10^7
In short, 10 million = 10^7.
Or put another way, 10 million = 10,000,000 = 1 followed by 7 zeros. The exponent tells us how many zeros are tacked onto the 1.
a = 2*10^(-3) = length of one ant in meters
b = 10^7 = number of ants
c = a*b = total length, in meters, of that number of ants assuming no gaps or overlaps.
We also assume the ants form a straight line.
c = a*b
c = 2*10^(-3)*10^7
c = 2*10^(-3+7)
c = 2*10^(4)
c = 2*10,000
c = 20,000 meters
Notes:- I used the exponent rule a^b*a^c = a^(b+c).
- 20,000 meters = 20 kilometers
- 20 kilometers = 12.4274 miles approximately
- 20 kilometers = 6,5616.7979 feet approximately
- 2*10^(-3) meters = 0.002 meters = 2 mm
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
A sugar ant is approximately 2 × 10^−3 meters long. If you put 10 million sugar
ants in a line, what is the distance from end to end?
200 meters
2,000 meters
20,000 meters
200,000 meters
2 x 10- 3 x 10,000,000
2 x 10- 3 x 107 --- Converting 10,000,000 to EXPONENT with base 10
2 x 10(- 3 + 7) ----- Adding EXPONENTS, when multiplying same base
2 x 104 = 2 x 10,000 = 20,000 meters
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