# 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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