# How Do You Arrange Decimals From Smallest To Largest?

0.075, 0.09, 0.6, 0.65, 0.653, 0.8
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Line up the decimal points. The number with the non-zero digit farthest to the left is the largest. If there is more than one number with such a digit in the same place, the one with the highest digit value is the largest. If the highest digits are the same, resolve the conflict by looking at the next digit to the right.

For example, 100.0 is larger than 99.0 because it has 3 digits to the left of the decimal point, whereas 99.0 only has two such digits.

180.0 is larger than 170.0 because the digit to the right of the leftmost digit is larger, and the leftmost digits are the same.

0.1 (= 0.100) is larger than 0.099 for the same reason that 100 is larger than 99. You can extend decimal numbers with zeros to the right of the rightmost decimal digit as much as necessary to make them the same length for comparison.

0.116 is larger than 0.115 because digits to the left of the 5 and 6 all agree, and 6 is larger than 5.

0.06 is smaller than 0.5 because its leftmost non-zero digit is further to the right in relationship to the decimal point.

Once you know the largest of a pair of numbers, you can put them in any order you like: Largest to smallest, or smallest to largest.

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From smallest to largest 4.2, 8.3, 7.9, 9.3, 0.5, 1.6, 5.6, 6.0, 3.4, 10.5
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What decimals would you like to arrange? What does it mean to "arrange" a decimal?

In our numbering scheme, the value associated with a digit depends on its place in the number. This is called "place value." It depends on how far the digit is from the decimal point. The place value gets larger as you get farther to the left of the decimal point, and smaller as you go farther to the right.

In money terms,
\$100.00 represents one hundred dollars
\$10.00 represents ten dollars, 1/10 of 100 dollars
\$1.00 represents one dollar, 1/10 of 10 dollars
\$0.10 represents ten cents, 1/10 of 1 dollar
\$0.01 represents one cent, 1/10 of .1 dollars or 1/100 of 1 dollar

As straight numbers, not money, the same relationships apply. The number .001 would have 1/10 the value of .01, and so on. Something like .023 could be considered as 2/100 + 3/1000, or, equivalently, 23/1000.

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.401, .40101, .4013, .4030, .40303, .4031
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Yes, that's easy: 1)0.035 2) 0.05 3)0.0503 4) 0.3 yay for the dewey decimal system!
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12.46
12.281
12.728
12.5
12'058
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