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5.31 miles  + 1.1 new miles; from I-70 near Stapleton to I-25 at US 36 (Boulder Turnpike).
Colorado's original proposal for I-270 was to designate it part of I-425, a connector from I-70 to I-25. The proposed I-80S (today's I-76) would end at I-425.
However, the Bureau of Public Roads recommended having I-80S terminate at I-25 instead of I-425; and then I-425 would end at I-80S. Since it was now completely separate from I-25, the Colorado Department of Highways recommended changing I-425's number to 270. This was approved on Feb. 26, 1959. 
I-270 was complete by the late 1960s or so, from I-70 to I-76. Motorists headed to Boulder from this area funneled onto I-76, then turned north on I-25 before making a quick turn onto US 36. This was quite a mess, and the state planned a small-scale improvement with a big payoff.
Extension to I-25 helps sort out 25/76/36 mess
The idea: help people bypass the I-25/76 interchange by extending I-270, which ended at I-76, to the Boulder Turnpike, which ended at I-25. Now the 1.1-mile extension of I-270 continues seamlessly onto US 36.
In fall 1999, there was a westbound extension to a new ramp (called "Exit 0") onto I-25 north. In February 2001, the westbound lanes were completely open; and on Aug. 17, 2003, the eastbound lanes opened. Two flyover ramps remain to be built as of August 2003: southbound I-25 to eastbound I-270, and eastbound I-270 to eastbound I-76. 
Denver Post writer Ricky Young states that renaming the US 36 freeway as an extension of I-270 was considered, but this apparently was not followed through.
On April 7, 2000, AASHTO approved the westward extension of the I-270 designation to I-25. 
34.40 miles ; from I-70 in Frederick to I-495 (the Capital Beltway) in Bethesda. The highway has seen a few numbering changes, and a controversial extension inside I-495 was cancelled in 1975.
Inside the Beltway: A direct route to central D. C. proposed
Proposed as a "new route [US] 240" in July 1957, I-270 was originally planned to be called I-70S and to extend into Washington, D. C. The exact location was under discussion. Circa 1958 and 1959, I-70S was to end at I-66 near Georgetown.  Later, a terminus at I-95 near Takoma Park was considered. All plans met considerable opposition, and in 1975 I-270 inside the Beltway was cancelled. 
Outside the Beltway: upgrading US 240; the original (short) I-270
I-270's ancestor was the 4-lane Washington National Pike (US 240), which was completed from Frederick to Connecticut Ave. near Chevy Chase in the late 1950's. The US 40 bypass of Frederick, also 4 lanes, opened at the same time.
Around 1961, US 240 became I-70S, and the Frederick bypass became I-70. What is now I-70 east of Frederick was called I-70N. The easternmost two miles of US 240 (through Rock Creek Park) was upgraded and became part of I-495. That explains the winding alignment of I-495 today in that area.
I-495 intersects I-270 at a large 3-way directional interchange, where I-495 and two legs or "wyes" of I-270 form a triangle. These are not just long ramps: each wye is over a mile long and has its own interchange with a local street. As the roads were built, the longer east wye carried I-70S and the shorter west wye was designated I-270. 
Scott Kozel recalls the I-270 trailblazer on the west wye, but the big overhead guide signs signed it southbound as 'TO I-495 SOUTH' and northbound as 'TO I-70S NORTH'.
I-70S becomes I-270
On May 18, 1975, the FHWA approved a request from the Maryland State Highway Administration to renumber I-70N and I-70S.  I-70N became part of the mainline I-70, I-70S became I-270, and the short I-270 wye became Spur 270. The year 1975 also marks the completion of the 26-mile upgrade of four-lane US 40 Baltimore National Pike east of Frederick.
Why did Baltimore get the main-line I-70 designation and Washington the spur I-270? Scott Kozel comments that although cities usually want the status of a main-line interstate, DC, with its center of federal government, might not have considered I-270 vs. I-70 to make much of a difference. (The timing of the cancellation of the I-270 extension inside the beltway may have had an effect as well).
David J. Edmonson points out Maryland state politics probably had an influence: "the one ironclad rule of Maryland politics, particularly at the time in question, is that whatever Baltimore wants, Baltimore gets. Even if the Washington suburbs had wanted the main line of I-70, they would have had no way to get it." 
In 1972, I-270 was widened to six lanes from the wye split near Tuckerman Lane to MD 118, a distance of 13 miles. In 1989, I-270 was widened to twelve lanes (2-4-4-2 configuration) from the wye split to I-370, and eight lanes from there to MD 118, a total of 13 miles. In 1997, widening to six lanes will be completed from MD 118 to MD 121, a distance of 3 miles. In 1997, widening to six lanes was completed on both wyes, with upgraded interchanges with I-495. This will complete the expansion of I-270 from I-495 to MD 121. Studies were underway to six-lane I-270 from MD 121 to Frederick.  After major reconstruction in the late 1980s, I-270 widens to 14 lanes near I-495. .
However, by 1999 the widened I-270 had already exceed traffic projections for 2010 in some segments. "We had five years of smooth sailing, which was wonderful," a service center director told the Washington Post, but congestion returned after that. The faster-than-expected traffic increase evoked mentions of induced demand or induced travel, the importance of which are debated among traffic professionals. 
The Maryland DOT official designation for the I-270 Spur is I-270Y. (For more fun, read about I-495X not far from there.) See also:
54.97 miles ; full beltway around Columbus. Partly done in 1965; finished in 1975 or 76.
The north side of I-270 underwent a $106M major widening, adding two lanes in each direction between US 33 in Dublin to OH 3 in Westerville. This was finished in 2001.
I-270 Missouri; Illinois
50.57 miles ; from I-55/255 in Mehlville, Mo. to I-55/70 near Troy, Ill. Serves St. Louis area. This road has been around since at least 1965; complete by 1974. the southern bypass, I-255, is considerably newer.
On July 31, 1958, Missouri presented a St. Louis beltway numbering plan to AASHO. Clockwise from the Illinois line, the beltway would be called I-255 up to I-55; I-144 between I-55 and I-70; and I-270 from I-70 continuing into Illinois. On Nov. 10, 1958, AASHO directed the state to change I-144 to I-244, since it was part of a bypass instead of a spur. 
In 1974, when I-244 was complete, Missouri deleted that number and incorporated the highway into an extended I-270. It looked like I-270 would soon encompass the entire loop: in 1978, the federal highway log reflected this, with 75.17 miles for I-270 and nothing for I-255.  The leftover part of I-270 not in the loop (between I-255 and I-55/70) was to be called I-870. 
However, I-870 was never designated, and I-255 remains as part of the beltway.