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Order decimals to thousandths

Ordering decimals to thousandths means comparing their values by aligning digits according to place value—ones, tenths, hundredths, and thousandths—rather than comparing individual digits or the apparent length of the notation. Learners interpret equivalent forms such as 0.7=0.70=0.7000.7 = 0.70 = 0.700, locate decimals on a number line, and arrange positive decimals with differing numbers of written decimal places, supporting precise comparison in measurement, fractions, and later proportional reasoning.

Detailed Explanation: Order decimals to thousandths

To order decimals to thousandths, line up the decimal points and compare digits by place value:

onestenthshundredthsthousandths\text{ones} \quad \text{tenths} \quad \text{hundredths} \quad \text{thousandths}

You can add zeros at the end of a decimal without changing its value. For example,

0.7=0.70=0.7000.7=0.70=0.700

Example: Order these decimals from least to greatest:

0.7,0.65,0.705,0.680.7,\quad 0.65,\quad 0.705,\quad 0.68

First, write each decimal to thousandths by adding zeros when needed:

0.7=0.7000.65=0.6500.705=0.7050.68=0.680\begin{aligned} 0.7&=0.700\\ 0.65&=0.650\\ 0.705&=0.705\\ 0.68&=0.680 \end{aligned}

Now compare the digits from left to right. All the numbers have 00 ones and 77 or 66 tenths.

  • (0.650)(0.650) and (0.680)(0.680) have 66 tenths, so they are less than the numbers with 77 tenths.
  • Between (0.650)(0.650) and (0.680)(0.680), compare the hundredths: (5<8)(5<8), so (0.650<0.680)(0.650<0.680).
  • Between (0.700)(0.700) and (0.705)(0.705), the tenths and hundredths are equal. Compare the thousandths: (0<5)(0<5), so (0.700<0.705)(0.700<0.705).

Therefore, from least to greatest:

0.65,0.68,0.7,0.705\boxed{0.65,\quad 0.68,\quad 0.7,\quad 0.705}

Remember: compare place values, not the number of digits. For instance, (0.7)(0.7) is greater than (0.68)(0.68) because (0.700>0.680)(0.700>0.680).

Learn by doing: Order decimals to thousandths

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    Decimals Comparisons - Thousandths

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