Comparing Decimals Practice

Look at the whole number part before examining the decimal digits. If the whole parts differ, you already know which positive number is larger. For example, 5.01 is greater than 4.99 because five whole units exceed four whole units. The longer or larger looking fractional part cannot overturn that difference. Only compare the fractional places when the whole parts are equal.

Read matching places from left to right. Compare tenths first, then hundredths, then thousandths if necessary. Stop at the first unequal pair of digits. In 0.64 and 0.67, the tenths match. The hundredths differ: four hundredths is less than seven hundredths. Therefore 0.64 < 0.67. Later places cannot reverse a difference already established in an earlier place.

When one number ends sooner, imagine or write a zero in each missing fractional place. Comparing 0.6 with 0.58 becomes easier as 0.60 and 0.58. Six tenths is greater than five tenths, so 0.6 is larger. The extra digit in 0.58 does not make it larger because those digits describe different sized parts of a whole.

Trailing zeros can also show that two written decimals are equal. The numbers 4.070 and 4.07 have the same whole part, tenths, and hundredths. The remaining thousandths digit is zero. No extra quantity has been added, so use the equals sign. A zero inside a number is different: removing the zero in 4.07 would produce 4.7 and change its value.

Choose the symbol only after deciding the relationship. The open side of < or > faces the larger number, and the pointed side faces the smaller one. Read your completed statement aloud, such as “zero point six is greater than zero point five eight.” If the symbols still feel confusing, write “larger,” “smaller,” or “equal” first and translate that decision into a symbol.