Name: Comparing numbers in different forms: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 34 s
Description: Which of the following numbers is the greatest? Try it, then watch the animated solution.

Numbers in different forms are hard to compare. Write every one as a decimal, then place them on a number line.

Convert:

\tfrac{2}{3} = 2 \div 3 = 0.666\ldots

and

68\% = 68 \div 100 = 0.68

.

0.69

is already a decimal.

For

\sqrt{0.5}

, square a guess:

0.7^2 = 0.49

, just under

0.5

. So

\sqrt{0.5}

is a bit more than

0.7

, about

0.707

.

On the number line:

0.666\ldots < 0.68 < 0.69 < 0.707

. The greatest is

\sqrt{0.5}

.

Traps:

0.69

looks biggest of the plain decimals, and the root of a number between

0

and

1

is bigger, not smaller.

Try it first