A structural steel fabricator cuts 30 pieces, each 18.6 centimeters long, from a 7.5-meter length of channel iron. Allowing 5.0 millimeters waste for each piece, what is the length in meters of channel iron left after all pieces have been cut? Round the answer to two significant digits.
The total length of the 30 pieces is 30 pieces * 18.6 cm = <<30*18.6=558>>558 cm.
Converting the length of the pieces to meters gives 558 cm * 1 m/100 cm = <<558*1/100=5.58>>5.58 m.
The total waste is 30 pieces * 5.0 mm/piece = 150 mm.
Converting the waste to meters gives 150 mm * 1 m/1000 mm = <<150*1/1000=0.15>>0.15 m.
The total length of channel iron used for the pieces and waste is 5.58 m + 0.15 m = <<5.58+0.15=5.73>>5.73 m.
The length of channel iron left after all the pieces have been cut is 7.5 m - 5.73 m = <<7.5-5.73=1.77>>1.77 m. Answer: \boxed{1.77}.
To find the total length of the channel iron needed for the 30 pieces, we need to calculate the total length of each piece plus the waste.
1. Calculate the total length of each piece:
Length of each piece = 18.6 centimeters = 0.186 meters (since 1 meter = 100 centimeters)
2. Calculate the total waste for each piece:
Waste for each piece = 5.0 millimeters = 0.005 meters (since 1 meter = 1000 millimeters)
3. Calculate the total length of the channel iron needed for all 30 pieces:
Total length of channel iron needed = (Length of each piece + Waste) * Number of pieces
= (0.186 + 0.005) * 30
= 0.191 * 30
= 5.73 meters
4. Calculate the length of channel iron left after all pieces have been cut:
Length of channel iron left = Total length of channel iron - Total length of channel iron needed
= 7.5 meters - 5.73 meters
= 1.77 meters
Rounded to two significant digits, the length of channel iron left after all pieces have been cut is 1.8 meters.
To find the length of the channel iron left after all the pieces have been cut, we first need to calculate the total length of all the pieces.
Each piece is 18.6 centimeters long, and there are 30 pieces. So the total length of all the pieces is:
30 pieces * 18.6 centimeters/piece = 558 centimeters
Now, we need to convert this length from centimeters to meters. There are 100 centimeters in a meter, so to convert centimeters to meters, we divide by 100:
558 centimeters / 100 = 5.58 meters
Next, we need to account for the waste. Each piece has a waste of 5.0 millimeters, and there are 30 pieces. So the total waste is:
30 pieces * 5.0 millimeters/piece = 150 millimeters
To convert millimeters to meters, we divide by 1000:
150 millimeters / 1000 = 0.15 meters
Finally, to find the length of the channel iron left after all the pieces have been cut, we subtract the total length of the pieces from the total waste:
7.5 meters - (5.58 meters + 0.15 meters) = 1.77 meters
Rounded to two significant digits, the length of the channel iron left after all the pieces have been cut is 1.8 meters.