Earths diameter is about 13,000 Kilometers. If a globe has a diameter of 0.5 meter, write the globe's scale as a ratio. What distance on Earth would 1 centimeter on the globe represent?
26000km/m * 1000 m/km = 26,000,000 to 1
1 cm * 26,000,000 = 26*10^6 cm
26*10^6 cm * 10^-2 m/cm * 10^-3 km/m
= 260 km
when doing unit conversions I multiply by quantities that are the same top and bottom but different units.
For example if I multiply a distance by 1000 m/km I do not change the distance, just the units from km to meters
The same in going from
cm to meters, * 1 meter/100 cm
and then meters to kilometers * 1 km/1000m
10^-2 = 1/10^2 = 1/100
10^-3 = 1/10^3 = 1/1000
10^6 = 1,000,000
can you explain that in 6th grade language please?
To find the scale of the globe, we need to compare the diameter of the globe to the diameter of the Earth.
Given:
Earth's diameter = 13,000 kilometers
Globe's diameter = 0.5 meter (convert to kilometers: 0.5 * 0.001 = 0.0005 kilometers)
The scale of the globe is the ratio of the size of the globe to the size of the Earth. In this case, the globe is smaller, so the ratio will be less than 1.
Scale = Globe's diameter / Earth's diameter
Scale = 0.0005 kilometers / 13,000 kilometers
Simplify the ratio:
Scale = 5 × 10^(-4) / 13 × 10^3
To divide the numbers written in scientific notation, we subtract the exponents:
Scale = 5 / 13 × 10^(-4-3)
Scale = 5 / 13 × 10^(-7)
So, the scale of the globe can be written as 5:13 × 10^(-7).
Now, to find what distance on Earth 1 centimeter on the globe represents, we can set up a proportion using the scale:
Scale = Globe distance / Earth distance
5:13 × 10^(-7) = 1 centimeter / x kilometers
To solve for x, we can cross multiply:
5x = 13 × 10^(-7) × 1
5x = 13 × 10^(-7)
Divide both sides by 5:
x = 13 × 10^(-7) / 5
x ≈ 2.6 × 10^(-7) kilometers
So, 1 centimeter on the globe represents approximately 2.6 × 10^(-7) kilometers on Earth.