Arrange the following numerical values in ascending order (from smallest to largest).

The correct ascending order is

\frac{2}{5}

0.6

\frac{7}{10}

, and

0.75

When converted to decimals, the values are

0.40

0.60

0.70

, and

0.75

. Arranging these from smallest to largest yields the correct sequence:

\frac{2}{5}

0.6

\frac{7}{10}

0.75

Convert the fractions into decimal format to establish a common baseline for comparison.

\frac{2}{5} = 0.4

and

\frac{7}{10} = 0.7

Decimals are often much easier to compare directly digit by digit than mixed formats.

Append trailing zeros to the decimal values to ensure they all have the same number of decimal places (two places, matching 0.75).

The values to compare are

0.40

0.60

0.70

, and

0.75

Aligning decimal places prevents magnitude confusion and makes visual comparison straightforward.

Order the standardized decimals from smallest to largest.

0.40 < 0.60 < 0.70 < 0.75

The question explicitly requires an ascending order.

Map the ordered decimals back to their original given forms.

\frac{2}{5} < 0.6 < \frac{7}{10} < 0.75

The final answer must be presented using the exact numbers provided in the question.

Converting fractions to decimals to evaluate and compare their magnitudes.

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