NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 4: Fractions & Decimals - Problems and Solutions
Question 76

Question. 76

Using the digits 1, 5, 3 and 8 once each, write the largest four-digit decimal number less than 1.

Answer:

\(0.8531\)

Detailed Answer with Explanation:

Goal: We need a number less than 1 that uses the digits 1, 5, 3, 8 exactly once, and has four digits after the decimal.

Any number less than 1 looks like:

\(0.\text{(tenths)(hundredths)(thousandths)(ten-thousandths)}\)

  1. Place the biggest digit in the tenths place to make the number as large as possible, but still less than 1.

    Biggest digit is \(8\).

    So tenths = \(8\), the number starts: \(0.8\dots\)

  2. Next biggest digit in the hundredths place.

    Remaining digits: \(5, 3, 1\).

    Choose \(5\).

    Now we have: \(0.85\dots\)

  3. Next, fill the thousandths place.

    Remaining digits: \(3, 1\).

    Choose \(3\).

    Now: \(0.853\dots\)

  4. Finally, fill the ten-thousandths place with the last digit.

    Last digit is \(1\).

    Complete number: \(0.8531\).

Why this is largest: A bigger digit earlier (like tenths) increases the value more than a bigger digit later (like thousandths). We placed digits in descending order: \(8\rightarrow5\rightarrow3\rightarrow1\).

Answer: \(0.8531\)

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