Zeros at the right end of a decimal

The idea

Zeros written at the right end of a decimal number leave its value unchanged, as they add only zero smaller parts; zeros placed between the decimal point and a digit move that digit to a smaller place value.

The zero dilemma

Sonu says 0.2 = 0.20 = 0.200. Zara thinks that putting zeros on the right side may change the value.

Who do you think is right?

• Sonu: the value stays the same
• Zara: extra zeros change the value
• It depends where the zero goes

Add zeros

Start with 0.2. Add a zero at the right end, or right after the point, and compare.

Look at the places

Writing each number place by place shows which ones are equal.

Zeros at the right end of a decimal leave its value unchanged, because they add only zero smaller parts: 0.2 = 0.20 = 0.200. Zeros between the decimal point and a digit move that digit to a smaller place value: 0.2, 0.02 and 0.002 are different.

• Number | Places
• 0.2 | 0 units, 2 tenths
• 0.20 | 0 units, 2 tenths, 0 hundredths
• 0.200 | 2 tenths, 0 hundredths, 0 thousandths
• 0.02 | 0 tenths, 2 hundredths
• 0.002 | 0 tenths, 0 hundredths, 2 thousandths

Notes

Zeros at the right end of a decimal do not change its value. Zeros between the point and a digit make that digit worth less.

Check yourself

Which of these is equal to 0.5?

Which of these is not equal to 3.4?

In 0.250, which digit is in the thousandths place?

Answer: 0

0.250 = 2 tenths, 5 hundredths and 0 thousandths. It equals 0.25.

Which is the biggest: 0.7, 0.07 or 0.007?

• 0.005. That is 5 thousandths, much smaller.
• 0.05. That is 5 hundredths. The zero after the point moved the 5 one place down.
• 0.50 — correct. Yes! 5 tenths and 0 hundredths is still 5 tenths.
• 3.04 — correct. Yes! The zero after the point pushes the 4 into the hundredths place.
• 3.40. This is equal: 4 tenths and 0 hundredths.
• 3.400. This is equal: the extra zeros are at the right end.
• 0.007. That is 7 thousandths, the smallest of the three.
• 0.07. That is 7 hundredths. 0.7 is 10 times as big.
• 0.7 — correct. Yes! 7 tenths is more than 7 hundredths or 7 thousandths.