Compare & round decimals

What is this skill?

Decimals extend place value to the right of the ones place: tenths, hundredths and thousandths. In fifth grade, children read and write decimals to the thousandths, compare them, and round them. The key fact is that a decimal is compared place by place from the left, the same way whole numbers are, and that the number of digits does not decide which number is bigger.

So 0.5 is greater than 0.45, even though 45 looks like a bigger number than 5. Written with matching places, 0.500 and 0.450 make the comparison plain. Rounding works the same way as with whole numbers. To round 3.46 to the nearest tenth, look at the hundredths digit. It is a 6, so the tenths digit goes up and the answer is 3.5. To round 0.347 to the nearest hundredth, look at the thousandths digit. It is a 7, so 0.34 becomes 0.35. A digit of 5 or more rounds up.

Why it matters

Money, measurement and sports statistics all use decimals, and children meet them every day. Comparing decimals correctly matters for things like prices per unit and race times. Rounding is how we estimate, and estimation is how we check calculations.

This is also the foundation for decimal operations later in the year. A child who is shaky on what each decimal place is worth will struggle to line up numbers for adding, subtracting and multiplying.

Common mistakes

• Believing the longer decimal is bigger, so 0.45 seems bigger than 0.5 because 45 is bigger than 5. Adding a zero (0.50) usually fixes the picture.
• Reading 0.45 as “forty-five” and forgetting what the digits are worth. Saying “forty-five hundredths” out loud keeps the place in mind.
• Rounding by looking at the wrong digit. To round to the tenths place, the digit to check is the one just to its right, in the hundredths place, and no other.
• Dropping the trailing zero when rounding. 2.96 to the nearest tenth is 3.0, which is the same value as 3, and either is correct.
• Mixing up the names of the places: tenths versus tens, hundredths versus hundreds.

How to help at home

• Use money first. $0.50 versus $0.45 is an easy comparison for most children, and the same reasoning transfers to any decimal.
• Practice “pad with zeros.” Ask your child to rewrite 0.5 and 0.45 with the same number of places, then compare.
• Draw a number line from 0 to 1 with ten parts and mark a decimal on it. Then zoom in on one part to show hundredths.
• Round things you see: a gas price per gallon, a race time, a ruler reading in centimeters.
• Ask “which digit decides?” before any rounding problem. Naming it out loud is half the skill.

Worked examples

These are real questions from the Tutorsaurus compare & round decimals practice, with the answers worked out.

1. Example 1

   6.959 ? 6.96

   Choices: >, <, =

   Answer: <. Line up the decimal points and compare place by place: 6.959 < 6.96.

2. Example 2

   Round 3.518 to the nearest tenth.

   Answer: 3.5. Look at the hundredths digit, 1. Less than 5, so keep the digit and drop the rest: 3.5.

3. Example 3

   Round 3.384 to the nearest whole number.

   Answer: 3. Look at the tenths digit, 3. Less than 5, so keep the digit and drop the rest: 3.