Using the digits 2, 4, 5 and 3 once, write the smallest four-digit decimal number (less than 1).
\(0.2345\)
Step 1: Understand the form.
The number is less than 1, so it looks like: (0.abcd)
Here, (a) is the tenths place, (b) is the hundredths place, (c) is the thousandths place, and (d) is the ten-thousandths place.
Step 2: Goal — make the smallest number.
To make a decimal as small as possible, put the smallest available digit in the leftmost place first (the tenths place), then the next smallest to the right, and so on.
Step 3: Arrange the given digits.
Digits to use once each: (2,,3,,4,,5)
Smallest is (2) ⇒ put (2) in the tenths place: (0.2)
Next smallest is (3) ⇒ put (3) in the hundredths place: (0.23)
Next is (4) ⇒ put (4) in the thousandths place: (0.234)
Last digit is (5) ⇒ put (5) in the ten-thousandths place: (0.2345)
Step 4: Final answer.
(0.2345)
Check:
All digits (2,3,4,5) are used once, and the number is less than (1). Any other order would put a bigger digit earlier and make a larger number.