# 93 Million Miles To Meters

how does one convert 93 million miles to meters using (A)power of ten and (B)a metric prefix?

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...

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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

Approved by eNotes Editorial Team