Compare Decimals Using Equal Place Values

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: Compare 0.7 and 0.65.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

Decimals should be compared by place value, not by counting digits. A trailing zero does not change a decimal’s value, so 0.6 can be written 0.60. Align tenths and hundredths, then use the first unequal place. A larger hundredths digit cannot outweigh a larger tenths value.

Rewrite both decimals to hundredths if needed. Compare tenths first, then hundredths if the tenths tie. Explain the comparison using equal wholes or number-line positions, keeping the unit of the compared measurements the same.

Use trailing zeros to align equal places. More written decimal digits do not automatically mean a larger number. Write both values in a Tenths/Hundredths chart using equal-size wholes.

1. Write both values in a Tenths/Hundredths chart using equal-size wholes.
2. Follow the worked example. Point to each number or shape feature and say what it tells you.
3. Rewrite both decimals to hundredths if needed.
4. Try the question and then the three practice questions. Check your answers and explain any change you make.

Check your reasoning

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Take it further

Compare 0.4 and 0.40. Expected: equal; the trailing zero changes notation, not value.

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