Fill in the Blanks!

Identifying Equivalent Decimals
Complete the table.

Equivalent decimals in different _.

8.24 - _
_+0.2+0.04 - 8+0.2+_+0.000
(8x1) + (2x0.1) + (4x0.01) - (8x1) + (2x0.1) + (4x0.01) + (0x0.001)

1 answer

To complete the table, it seems we're looking to express the equivalent decimals in different forms.

  1. Identifying Equivalent Decimals: The first blank should refer to forms or bases. This suggests we are comparing different representations of the same decimal.

  2. Filling in the blanks:

    • For "8.24 - _", we can express 8.24 as a decimal and find an equivalent representation. One option could be "8.240" or "8.24" itself, depending on the context.

    • For " _ + 0.2 + 0.04 - 8 + 0.2 + _ + 0.000", we need two values that when substituted maintain the equality. Here, we're already using 0.2 and 0.04. Notice that:

      • The left side contains the expression of 8.24.
      • The right side can be kept consistent by using 0.04 again since we initially have both 0.2 and 0.04 on the left side. That means the blanks can be filled in with "0.04" and "0.04".
  3. Final Expression:

    • The first blank is “forms”.
    • The fill-in for the first blank in "8.24 - _" could be “8.240”.
    • The two blanks in "_ + 0.2 + 0.04 - 8 + 0.2 + _ + 0.000" can both be filled with "0.04".

Thus, the completed components of your table may look like this:

  • Equivalent decimals in different forms.
  • 8.24 - 8.240
  • 0.04 + 0.2 + 0.04 - 8 + 0.2 + 0.04 + 0.000
  • (8 x 1) + (2 x 0.1) + (4 x 0.01) - (8 x 1) + (2 x 0.1) + (4 x 0.01) + (0 x 0.001).