Decimals: Tenths on a Grid (4th Grade)

What is it?

A decimal is another way to write a fraction. The first digit after the decimal point counts tenths, which are the parts you get when one whole is cut into 10 equal pieces. So 0.3 and 3/10 are the same amount, written two ways. A grid with 10 equal strips makes this easy to see: shade 3 strips and read it as 3 tenths. The point separates the whole numbers from the parts of one whole.

Step by step: 3/10 = 0.3

1. Start with 1 whole, cut into 10 equal parts. Each part is 1 tenth, or 1/10.
2. Shade 3 of the 10 parts.
3. 3 parts out of 10 is the fraction 3/10, read as "three tenths".
4. Write it as a decimal. The 0 before the point means no whole ones. The 3 after the point is the tenths place.
5. So 3/10 = 0.3. Read it as "three tenths".

Common mistakes

• Writing 3/10 as 0.03. The first place after the point is tenths, so 3 tenths is 0.3. Two places (0.03) means hundredths.
• Writing 3/10 as 3.10. The 3 is a part of one whole, not three wholes.
• Thinking 0.4 is smaller than 0.04 because it has fewer digits. 0.4 is 4 tenths, and 0.04 is only 4 hundredths.

Your turn

Here is a problem to try. Pause and let your child work it out before you check.

A bar is cut into 10 equal parts and 7 are shaded. What decimal is shaded?

Answer: 0.7 (seven tenths). 7 of 10 equal parts is 7/10, and 7/10 is written 0.7.

Practice at home

Fold a paper strip into 10 equal parts, or use a ruler: each centimeter on a 10 cm piece is one tenth of it. Color some parts and ask your child to say the fraction and then the decimal. Then point to a decimal like 0.6 on a number line from 0 to 1 and count the tenths together.