Question

Recall that with base ten blocks, 1 long = 10 units, 1 flat = 10 longs, and 1 block = 10 flats. Make all possible exchanges to obtain the fewest number of pieces and write the corresponding number in base eleven for the following sixty flats.

Answer 1

To convert sixty flats into the fewest number of base ten blocks, we exchange them for 6 blocks. The corresponding number of 60 in base eleven is '55'.

Step-by-step explanation:

To answer the question, we need to convert sixty flats to the smallest number of base ten blocks and then write the corresponding number in base eleven. With the given values that 1 long equals 10 units, 1 flat equals 10 longs, and 1 block equals 10 flats, it becomes a matter of applying place value knowledge with base ten blocks.

Sixty flats can be exchanged for 6 blocks since 1 block is equal to 10 flats. There are no remaining flats. When writing the number 60 in base eleven, we do not encounter any digits which require us to go beyond '10' in base ten. Therefore, the corresponding number in base eleven is simply '55', since 5 flats (50 units in base ten) plus 5 longs (10 units in base ten) equals 60 units in base ten.

We are not concerned with powers, decimal movement, unit conversions, or volumes—in this specific instance, we are dealing with integer values and place value exchanges in different number bases.