Questions regarding centimeters, kilometers, hectometer, dekameter, decimeter , millimeter?

Question

Need answers to be explained step by step for 6th grader
Examples: 1. 8cm = ___mm, 2.__ 8cm =____dm 3. 7m =____dekameter, 4. 9dam = ____km 5. 1,600mm = ____km
6. 5m =____dam 7. 9dekameter =_____cm 8.

Answer 1

The best way to understand this is to use division and conversion factors to make sure your units cancel. Writing out units and ensuring that they cancel will help you avoid simple mistakes, such as:

100 cm * 1 cm / 10 mm = 10 cm^2 / mm, which makes it clear that you're using the wrong factor. 100 cm is 1000 mm.

1.) 8 cm * 10 mm / cm = 80 mm. The cm on top and bottom of the fraction cancel, leaving you mm and your answer. The conversion factor 10 mm / cm is a mathematical way to state "There are 10 millimeters in 1 centemeter."

2.) To step up, use 1 dm / 10 cm as your conversion factor. 8 cm * 1 dm / 10 cm = 8/10 dm = .8 dm. The conversion factor 10 mm / cm is a mathematical way to state "In 1 decimeter, there are 10 centimeters."

3.) 1 dam / 10 m
4.) 1 km / 100 dam
5.) 1 km / 1,000,000 mm or 1 km / 1000 m * 1 m * 1000 mm (you can combine conversion factors if it helps you).
6.) 1 dam / 10 m
7.) 10 m / dam * 100 cm / 1m