93 Million Miles To Meters
how does one convert 93 million miles to meters using (A)power of ten and (B)a metric prefix?
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This uses unit-analysis, a skillset of dimensional analysis.
93000000 miles -> ? m
Convert to scientific notation
`9.3\times10^7 mi`
It is known that `10^-2 m = 1 cm`
`2.54cm = 1 \text(in)` exactly.
`1.2\times10^1 \text(in) = 1 ft` exactly.
`5.280\times10^3 ft = 1 mi` exactly.
Using these exact terms as fractions, we can arrange them to cancel out mi and be left with meters.
`(9.3\times10^7 mi)/1\times((5.280\times10^3ft)/(1 mi))\times((1.2\times10^1\text(in))/(1 ft))\times((2.54 cm)/(1\text(in)))\times((10^(-2)m)/(1 cm))`
Cancelling out units and multiplying we get:
`1.49668992\times10^(11) m`
exactly. or approximately `1.5\times10^11m`
Since 1 Gm = 10^9 m
Then `1.5\times10^(11) m rArr ? Gm`
`(1.5\times10^(11)m)/1\times((1 Gm)/(10^9 m))`
`=150 Gm`
Since `1 Tm = 10^3 Gm`
`1.5\times 10^2 Gm rArr ? Tm`
Using the same technique:
`0.15 Tm`
we know that 1 mile = 1609.34 meter, so
93 million miles * (1609.34 meter/ 1miles)
=149668992000 meter
=1.5*10^11 meter
B. 1 giga = 10^9
so
93 million miles = 149668992000 meter = 150 gigameter
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