Arranging Decimal Numbers
Arranging decimal numbers in order requires appending trailing zeros so all numbers have the same number of decimal places, then comparing digit by digit from left to right. In Grade 6 Saxon Math Course 1 (Chapter 5: Number and Operations), students pad shorter decimals with zeros (e.g., 2.5 becomes 2.50), compare the resulting numbers as whole numbers after ignoring the decimal point, then write the final ordered list without extra zeros. For 0.3, 0.25, 0.305: pad to 0.300, 0.250, 0.305; ordered from least to greatest: 0.250 < 0.300 < 0.305, written as 0.25, 0.3, 0.305.
Key Concepts
Property To arrange a set of decimal numbers, first write each number with the same number of decimal places by attaching trailing zeros. Then, arrange them in order from least to greatest based on their new forms, omitting the extra zeros in the final answer.
Examples Order $0.4, 0.05, 0.35$: Becomes $0.40, 0.05, 0.35$. The correct order is $0.05, 0.35, 0.4$. Order $0.8, 0.808, 0.08$: Becomes $0.800, 0.808, 0.080$. The correct order is $0.08, 0.8, 0.808$. Order $1.2, 1.23, 1.02$: Becomes $1.20, 1.23, 1.02$. The correct order is $1.02, 1.2, 1.23$.
Explanation Putting decimals in order is like lining up your friends by height. To make sure it is accurate, you first make them all stand on the same level ground! By adding trailing zeros to give every number the same number of decimal places, you can easily compare them and sort them from smallest to largest, just like with regular numbers.
Common Questions
How do you put decimal numbers in order from least to greatest?
Pad all decimals with trailing zeros to match the longest one. Compare digit by digit from left to right. The number with the smaller digit in the leftmost differing place is smaller.
Arrange 0.4, 0.04, and 0.44 from least to greatest.
Pad: 0.40, 0.04, 0.44. Comparing tenths: 0.04 has 0 tenths (smallest), 0.40 has 4 tenths, 0.44 has 4 tenths. In hundredths: 0.40 < 0.44. Order: 0.04, 0.4, 0.44.
Does adding trailing zeros to a decimal change its value?
No. 0.5, 0.50, and 0.500 are equal. Trailing zeros are only used temporarily to aid comparison.
How do you compare 1.6 and 1.59?
Pad 1.6 to 1.60. Compare hundredths: 1.60 vs 1.59. Since 60 > 59, then 1.6 > 1.59.
Arrange 3.2, 3.02, 3.22 from greatest to least.
Pad: 3.20, 3.02, 3.22. Order greatest to least: 3.22, 3.20, 3.02, i.e., 3.22, 3.2, 3.02.