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Create a 10-digit number using digits 0-9 exactly once. The first digit cannot be '0'. Find the smallest and largest such numbers.

Mathematics

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Answers

2 parts
a

1,023,456,789\text{1,023,456,789}

b

9,876,543,210\text{9,876,543,210}

Step-by-step solution

6 steps

ଏଠାରେ 10 ଅଙ୍କ ବିଶିଷ୍ଟ ସଂଖ୍ୟା ଗଠନ କରିବାକୁ ହେବ, ଯେଉଁଥିରେ 0 ରୁ 9 ପର୍ଯ୍ୟନ୍ତ ସମସ୍ତ ଅଙ୍କ ଥରେ ବ୍ୟବହାର ହେବ ଏବଂ ପ୍ରଥମ ଅଙ୍କ '0' ହେବ ନାହିଁ।

Part a· 3 steps

ଛୁଦ୍ରତମ ପୂର୍ଣ୍ଣ ସଂଖ୍ୟା (Smallest whole number)

ସବୁଠାରୁ ଛୋଟ 10-ଅଙ୍କ ବିଶିଷ୍ଟ ସଂଖ୍ୟା ଗଠନ କରିବା ପାଇଁ, ପ୍ରଥମ ଅଙ୍କ '0' ହୋଇପାରିବ ନାହିଁ। ତେଣୁ, ପ୍ରଥମ ଅଙ୍କ '1' ହେବ। ବାକି ଅଙ୍କଗୁଡ଼ିକୁ (0, 2, 3, 4, 5, 6, 7, 8, 9) ବୃଦ୍ଧି କ୍ରମରେ ସଜାନ୍ତୁ।

  1. ପ୍ରଥମ ଅଙ୍କ '1' ବାଛନ୍ତୁ।

  2. ବାକି 9ଟି ଅଙ୍କ (0, 2, 3, 4, 5, 6, 7, 8, 9) କୁ ବୃଦ୍ଧି କ୍ରମରେ ସଜାନ୍ତୁ।

  3. ସଂଖ୍ୟାଟି ହେବ

    1,023,456,7891,023,456,789

    The smallest 10-digit number is 1,023,456,789\boxed{\text{1,023,456,789}}.

Part b

9,876,543,210\text{9,876,543,210}

ବୃହତ୍ତମ ପୂର୍ଣ୍ଣ ସଂଖ୍ୟା (Largest whole number)

ସବୁଠାରୁ ବଡ଼ 10-ଅଙ୍କ ବିଶିଷ୍ଟ ସଂଖ୍ୟା ଗଠନ କରିବା ପାଇଁ, ପ୍ରଥମ ଅଙ୍କ ସବୁଠାରୁ ବଡ଼ ହେବ।

  1. ପ୍ରଥମ ଅଙ୍କ '9' ବାଛନ୍ତୁ।

  2. ବାକି 9ଟି ଅଙ୍କ (0, 1, 2, 3, 4, 5, 6, 7, 8) କୁ ହ୍ରାସ କ୍ରମରେ ସଜାନ୍ତୁ।

  3. ସଂଖ୍ୟାଟି ହେବ

    9,876,543,2109,876,543,210

    The largest 10-digit number is 9,876,543,210\boxed{\text{9,876,543,210}}.

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