Decimals (tenths, hundredths)

What is this skill?

A decimal is another way to write a fraction whose denominator is 10, 100 and so on. In fourth grade children connect tenths and hundredths to decimals: 4/10 is 0.4, and 37/100 is 0.37. The dot is the decimal point, and the digits to its right are places that continue the pattern of place value, each one a tenth of the one before.

The first place after the point is tenths, and the second is hundredths. That is why 0.5 means 5 tenths and 0.05 means 5 hundredths. Children also compare decimals, writing >, < or = between numbers like 0.53 and 0.54. The method is the one they know for whole numbers: compare the leftmost place where the numbers differ, tenths first, then hundredths. Money is the everyday model, since a dime is one tenth of a dollar and a penny is one hundredth. Children who can say “thirty-seven hundredths” aloud usually write 0.37 with confidence.

Why it matters

Decimals are everywhere outside the classroom: prices, measurements, sports times, and the display on a calculator. Seeing them as part of place value, not a separate topic, makes them much easier, and it lays the base for fifth-grade work with decimal operations.

The connection to fractions matters too. When a child sees that 0.3 and 3/10 are two names for one amount, both ideas become more solid. Comparing decimals is also a place where intuition from whole numbers can mislead, so it is worth getting right early.

Common mistakes

• Thinking a longer decimal is larger because it has more digits. 0.5 is greater than 0.28, even though 28 is more than 5.
• Writing 7/100 as 0.7. Hundredths need two places, so it is 0.07.
• Reading 0.45 as “zero point forty-five” without seeing what it means. Saying “forty-five hundredths” makes the fraction obvious.
• Dropping the zero placeholder, so 0.05 turns into 0.5.
• Ignoring the decimal point and lining up digits from the right when comparing.

How to help at home

• Use money. A dime is $0.10 and a penny is $0.01. Ask how many cents make $0.37, and how many dimes and pennies that is.
• Draw a 10 by 10 grid. Shade 37 squares and write the amount as a fraction and a decimal.
• Read decimals with the place value name: say “three tenths” rather than “point three.”
• Compare real numbers: gas prices, race times, a kitchen scale reading.
• Line up two decimals one above the other, adding a zero to the shorter one, before comparing.

Worked examples

These are real questions from the Tutorsaurus decimals (tenths, hundredths) practice, with the answers worked out.

1. Example 1

   0.53 ? 0.54

   Choices: >, <, =

   Answer: <. Compare tenths first, then hundredths. 0.53 < 0.54.

2. Example 2

   Write 4/10 as a decimal.

   Answer: 0.4. 4 tenths is 0.4.

3. Example 3

   Write 3/10 as a decimal.

   Answer: 0.3. 3 tenths is 0.3.