Equivalent decimals

key notes :

What are equivalent decimals?

Equivalent decimals are decimal numbers that have the same value. For example, 0.5 and 0.50 are equivalent decimals. You can see in the models below that five-tenths and fifty-hundredths take up the same amount of space.

Image on the left: A rectangle split into tenths, with five of the tenths shaded in. This rectangle is labeled with the decimal zero point five and the fraction five tenths.
Image on the right: A rectangle split into hundredths, with fifty of the hundredths shaded in. The rectangle is labeled with the decimal zero point five zero and the fraction fifty hundredths. The label also shows that the fraction fifty hundredths equals the fraction five tenths.

When you place zeros to the right of a decimal, its value stays the same. These zeros are called trailing zeros and do not change the value of the number.

0.8=0.80=0.800

Image on the left: A rectangle split into tenths, with three of the tenths shaded in. This rectangle is labeled with the decimal zero point three and the fraction three tenths.
Image on the right: A rectangle split into hundredths, with three of the hundredths shaded in. The rectangle is labeled with the decimal zero point zero three and the fraction three hundredths.

How can you make equivalent decimals?

You can make an equivalent decimal by placing zeros at the end of the decimal.

The decimal sixteen point eight, with an empty space after the eight. This decimal is followed by the equals sign and the decimal sixteen point eight zero zero. There is an arrow from the empty space on the left side of the equation to the zeros on the right side of the equation.
Image on the left: The decimal four point three one, with an empty space after the one. This decimal is followed by the equals sign and the decimal four point three one zero. There is an arrow from the empty space on the left side of the equation to the zero on the right side of the equation.

Annexing zeros, or placing zeros at the end of the decimal number, can be helpful when adding, subtracting, multiplying, or dividing decimals.

Learn with an example

🎯 Which decimal is equivalent to 50.7?

  • 17.0
  • 57.0
  • 50.70
  • 55.70
  • Write 1 extra zero to the right of 50.7:
  • 50.7 → 50.70
  • 50.7 and 50.70 are equivalent decimals.

🎯 Are 0.10 and 0.1 equivalent decimals?

  • yes
  • no
  • Write 1 extra zero to the right of 0.1:
  • 0.1 → 0.10
  • 0.10 and 0.1 are equivalent decimals.

🎯 Are 3.8 and 3.80 equivalent decimals?

  • yes
  • no
  • Write 1 extra zero to the right of 3.8:
  • 3.8 → 3.80
  • 3.8 and 3.80 are equivalent decimals.

Let’s practice!