Inequalities with decimals

When two decimals are compared, the digits are matched place by place, not counted. 2,524.0001201 and 2,524.00013 agree through the thousandths, and the ten-thousandths place holds a 1 in both. The hundred-thousandths place decides, 2 against 3, so the longer number loses.

The page keeps the whole-number part identical in most pairs, so your child has to read past the decimal point every time, sometimes six places deep, as in 0.000111 against 0.000101. Two pairs are equal on purpose, a good test of reading decimals digit by digit.

The standard is 5.NBT.A.3: compare two decimals to thousandths with the greater-than, equal and less-than symbols. The longer pairs stretch it past thousandths.

A note for parents: in the true-or-false part of page 1, the boxes between the numbers are empty, so the statements cannot be judged. Copy the signs from page 2 first: 0.20100 < 0.201101, 735.6751 < 735.6755, 11.0005 > 11.0015, 5.2035 < 5.2035, 9,251.21000103 < 9,251.2100011, and an equal sign for 3,256.025. In the top part, 60622211 is missing its point; read it as 606.22211.

Then ask, "Where do these two numbers first disagree?" The likely slip is 9,251.21000103, which looks bigger because it is longer. Ask your child to slide a finger under each place until the digits differ.

For 5.2035 < 5.2035, ask, "Can a number be less than itself?"

Swim and track results are posted to hundredths of a second, and a race can be won by 0.01. Look up a sport result with your child and compare two times digit by digit, out loud. At the store, compare two unit prices on the shelf labels, such as 0.125 and 0.13 dollars per ounce, the same way.

How Much Is a Million? by David M. Schwartz stretches place value until a child can feel how big a million is. After reading it, ask which is smaller, a millionth or a thousandth.

Praise the effort: "You checked every place before you picked a sign." The next sheet, rounding decimals, uses the same place-by-place reading to decide where a number lands.