Decimals
Lessons in this chapter
About Decimals
Decimals extends place value to the right of the ones column, which is the last structural extension of the number system kids meet in elementary school.
Express Tenths as Decimals and Express Hundredths as Decimals continue the pattern established years earlier. Each place is a tenth of the one to its left, so after ones come tenths and then hundredths, and the decimal point simply marks where the ones stop.
Convert Decimals to Fractions makes the link explicit: 0.7 is seven tenths and 0.43 is forty-three hundredths. Decimals are fractions with denominators fixed at powers of ten, which is why they can be written in a line.
Represent Decimals on a Number Line and Compare and Order Decimals tackle the big misconception. Kids read 0.45 as larger than 0.5 because 45 is larger than 5, and the number line is the fastest cure, since 0.5 is plainly further right.
Add and Subtract Decimals brings the arithmetic, with one rule: line up the decimal points. That is the place value alignment from every addition chapter, now with a visible marker.
All six lessons open as a 4th grade math worksheet in the page. Convert Decimals to Fractions, Compare and Order Decimals and Add and Subtract Decimals each set math problems that are worked one at a time and scored as you answer them. They are free to try, with no login needed for your first 3.
Frequently asked questions
Express Tenths as Decimals and Express Hundredths as Decimals continue the place value pattern to the right of the ones column, and Convert Decimals to Fractions makes the link explicit. Represent Decimals on a Number Line and Compare and Order Decimals tackle the usual misconception that 0.45 is larger than 0.5, and Add and Subtract Decimals closes the chapter. Decimal notation for fractions and comparing decimals sit in Number and Operations with Fractions (4.NF); adding and subtracting decimals is something the Common Core does not ask for until 5th grade, in Number and Operations in Base Ten (5.NBT).
A way of writing fractions with denominators of ten, a hundred and so on, using places to the right of the decimal point. 0.7 is seven tenths.
Because they compare 45 with 5 as whole numbers. But 0.5 is five tenths, which is fifty hundredths, so it is larger. The number line settles it instantly.
Read it aloud. 0.43 is forty-three hundredths, which is 43 over 100. The name of the last place gives the denominator.
Line up the decimal points so each place sits under its match. It is the same place value alignment as any column sum, just with a visible marker.
They continue it. Each place is a tenth of the one to its left, so ones are followed by tenths and then hundredths. The pattern never changes.