How to Compare Decimals

Read,3 minutes

To compare decimals, compare digits by place value from left to right. The places after the decimal point are tenths, hundredths, thousandths, and so on. A zero at the end of a decimal does not change its value, so \(4.5=4.50=4.500\).

Use this reliable method: line up the decimal points, add trailing zeros if helpful, then compare the first place where the digits are different. The number with the larger digit in that first different place is greater.

Examples

Example 1: Compare \(6.07\) and \(6.7\). Write \(6.7\) as \(6.70\). Since \(07<70\) hundredths, \(6.07<6.7\).

Example 2: Compare \(0.304\) and \(0.34\). Write \(0.34\) as \(0.340\). Since \(304<340\) thousandths, \(0.304<0.34\).

Example 3: Compare \(-1.2\) and \(-1.05\). Both are negative, so the number farther from zero is smaller. Since \(1.2>1.05\), \(-1.2<-1.05\).

Practice Exercises

1) Compare \(0.4\) and \(0.7\).

2) Compare \(0.35\) and \(0.3\).

3) Compare \(2.08\) and \(2.8\).

4) Compare \(5.120\) and \(5.12\).

5) Order \(0.9,\ 0.09,\ 0.99\) from least to greatest.

6) Compare \(3.456\) and \(3.465\).

7) Which is greater, \(12.04\) or \(12.004\)?

8) Order \(6.7,\ 6.07,\ 6.707,\ 6.77\) from greatest to least.

9) Compare \(-0.4\) and \(-0.35\).

10) Compare \(0.125\) and \(\frac{1}{8}\).

11) Compare \(4.2\) and \(4\frac{1}{5}\).

12) Which is closest to \(0.5\): \(0.49,\ 0.509,\ 0.52\)?

13) Place \(7.031,\ 7.13,\ 7.103,\ 7.013\) in increasing order.

14) Compare \(0.333\) and \(\frac{1}{3}\).

15) A runner finishes in \(12.06\) seconds and another in \(12.6\) seconds. Which time is shorter?

16) Compare \(45.099\) and \(45.1\).

17) Find a decimal with two decimal places between \(1.26\) and \(1.27\).

18) Order \(-2.5,\ -2.05,\ -2.55,\ -2.15\) from least to greatest.

19) Compare \(0.0205\) and \(0.025\).

20) Which number is greatest: \(\frac{7}{8},\ 0.86,\ 0.8751,\ 0.0875\)?

Answers

1) Write both to tenths: \(0.4\) and \(0.7\). Since \(4<7\), \(0.4<0.7\).

2) Write \(0.3\) as \(0.30\). Compare hundredths: \(35>30\), so \(0.35>0.30\). Therefore \(0.35>0.3\).

3) Write \(2.8\) as \(2.80\). The whole parts are both \(2\). Compare hundredths: \(08<80\), so \(2.08<2.8\).

4) Trailing zeros do not change a decimal: \(5.120=5.12\). The numbers are equal.

5) Use the same number of decimal places: \(0.90,\ 0.09,\ 0.99\). Since \(09<90<99\), the order is \(0.09,\ 0.9,\ 0.99\).

6) The ones, tenths, and hundredths match until the hundredths place: \(3.456\) has \(5\) hundredths and \(3.465\) has \(6\) hundredths. Since \(5<6\), \(3.456<3.465\).

7) Write \(12.04\) and \(12.004\). The whole parts are equal. In the tenths place both have \(0\). In the hundredths place \(4>0\), so \(12.04>12.004\).

8) Write each to thousandths: \(6.700,\ 6.070,\ 6.707,\ 6.770\). From greatest to least: \(6.770,\ 6.707,\ 6.700,\ 6.070\), so \(6.77,\ 6.707,\ 6.7,\ 6.07\).

9) For negative decimals, the number closer to zero is greater. Since \(-0.35\) is closer to zero than \(-0.4\), \(-0.4<-0.35\).

10) Convert the fraction: \(\frac{1}{8}=0.125\). The decimal \(0.125\) equals \(0.125\), so the numbers are equal.

11) Convert the mixed number: \(4\frac{1}{5}=4+0.2=4.2\). Therefore \(4.2=4\frac{1}{5}\).

12) Find each distance from \(0.5\): \(|0.49-0.5|=0.01\), \(|0.509-0.5|=0.009\), and \(|0.52-0.5|=0.02\). The smallest distance is \(0.009\), so \(0.509\) is closest.

13) Write all to thousandths: \(7.031,\ 7.130,\ 7.103,\ 7.013\). Compare the decimal parts \(013<031<103<130\). Increasing order: \(7.013,\ 7.031,\ 7.103,\ 7.13\).

14) The fraction \(\frac{1}{3}=0.333\ldots\). The decimal \(0.333\) stops after three \(3\)s, so \(0.333<0.333\ldots\). Therefore \(0.333<\frac{1}{3}\).

15) In a race, the smaller time is faster. Compare \(12.06\) and \(12.60\). Since \(06<60\) hundredths, \(12.06<12.6\), so \(12.06\) seconds is shorter.

16) Write \(45.1\) as \(45.100\). Compare \(45.099\) and \(45.100\). Since \(099<100\), \(45.099<45.1\).

17) Numbers with two decimal places move by hundredths. Between \(1.26\) and \(1.27\) there is no two-decimal-place number, because consecutive hundredths have no hundredth between them.

18) For negatives, farther left on the number line is least. Write the values in order: \(-2.55<-2.50<-2.15<-2.05\). So the order is \(-2.55,\ -2.5,\ -2.15,\ -2.05\).

19) Write \(0.025\) as \(0.0250\). Compare \(0.0205\) and \(0.0250\). In the thousandths place \(0<5\), so \(0.0205<0.025\).

20) Convert \(\frac{7}{8}\) to a decimal: \(7\div 8=0.875\). Compare \(0.875,\ 0.86,\ 0.8751,\ 0.0875\). Since \(0.8751\) is slightly greater than \(0.875\), the greatest number is \(0.8751\).

Free printable Worksheets