Explore · MATH-5B-C09-L03-OPEN
Compare 0.25 and 0.256 using < or >.
Singapore Math 5B · Original independent course
Comparing Decimals
Watch for: Assuming the decimal with more digits is larger.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C09-L03-PREREQ
Which is larger, 0.5 or 0.45?
Show worked answer (after attempting)
Answer: 0.5
Write 0.5 as 0.50, and compare 50 hundredths to 45 hundredths.
Understand the idea
Compare and order decimals to thousandths using same-sized units and number lines. The essential earlier idea is: 5A large-number comparison, decimal place value.. The model below will always use the actual quantities from the worked problem. Check assuming the decimal with more digits is larger when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C09-L03-Q01
Compare 0.243 and 0.249 using < or >.
Solution: 0.243 < 0.249
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 243 and 249.
Worked example 2 · MATH-5B-C09-L03-Q02
Two rain gauges read 0.243 L and 0.249 L. Which contains more?
Solution: 0.249 L
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 243 and 249.
Worked example 3 · MATH-5B-C09-L03-Q03
Order 0.243 and 0.21 from greatest to least and explain.
Solution: 0.243, 0.21
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 243 and 210.
Check understanding
1 · MATH-5B-C09-L03-Q04
Compare 0.25 and 0.256 using < or >.
Show worked answer (after attempting)
Answer: 0.25 < 0.256
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 250 and 256.
2 · MATH-5B-C09-L03-Q05
Two rain gauges read 0.25 L and 0.256 L. Which contains more?
Show worked answer (after attempting)
Answer: 0.256 L
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 250 and 256.
3 · MATH-5B-C09-L03-Q06
Order 0.25 and 0.217 from greatest to least and explain.
Show worked answer (after attempting)
Answer: 0.25, 0.217
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 250 and 217.
Guided practice
1 · MATH-5B-C09-L03-Q07
Compare 0.257 and 0.263 using < or >.
Show worked answer (after attempting)
Answer: 0.257 < 0.263
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 257 and 263.
2 · MATH-5B-C09-L03-Q08
Two rain gauges read 0.257 L and 0.263 L. Which contains more?
Show worked answer (after attempting)
Answer: 0.263 L
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 257 and 263.
3 · MATH-5B-C09-L03-Q09
Order 0.257 and 0.224 from greatest to least and explain.
Show worked answer (after attempting)
Answer: 0.257, 0.224
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 257 and 224.
4 · MATH-5B-C09-L03-Q10
Compare 0.264 and 0.27 using < or >.
Show worked answer (after attempting)
Answer: 0.264 < 0.27
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 264 and 270.
Independent practice
1 · MATH-5B-C09-L03-Q11
Two rain gauges read 0.264 L and 0.27 L. Which contains more?
Show worked answer (after attempting)
Answer: 0.27 L
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 264 and 270.
2 · MATH-5B-C09-L03-Q12
Order 0.264 and 0.231 from greatest to least and explain.
Show worked answer (after attempting)
Answer: 0.264, 0.231
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 264 and 231.
3 · MATH-5B-C09-L03-Q13
Compare 0.271 and 0.277 using < or >.
Show worked answer (after attempting)
Answer: 0.271 < 0.277
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 271 and 277.
4 · MATH-5B-C09-L03-Q14
Two rain gauges read 0.271 L and 0.277 L. Which contains more?
Show worked answer (after attempting)
Answer: 0.277 L
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 271 and 277.
5 · MATH-5B-C09-L03-Q15
Order 0.271 and 0.238 from greatest to least and explain.
Show worked answer (after attempting)
Answer: 0.271, 0.238
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 271 and 238.
6 · MATH-5B-C09-L03-Q16
Compare 0.278 and 0.284 using < or >.
Show worked answer (after attempting)
Answer: 0.278 < 0.284
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 278 and 284.
7 · MATH-5B-C09-L03-Q17
Two rain gauges read 0.278 L and 0.284 L. Which contains more?
Show worked answer (after attempting)
Answer: 0.284 L
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 278 and 284.
8 · MATH-5B-C09-L03-Q18
Order 0.278 and 0.245 from greatest to least and explain.
Show worked answer (after attempting)
Answer: 0.278, 0.245
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 278 and 245.
Challenge and error analysis
1 · MATH-5B-C09-L03-ERR1
The assigned question is: “Two rain gauges read 0.299 L and 0.305 L. Which contains more?” A learner wrote: “I compared 0.299 only by its first digit and recorded 0.405 L.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 0.305 L
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 0.305 L. Recompute from the given data: Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 299 and 305.
2 · MATH-5B-C09-L03-ERR2
The assigned question is: “Order 0.299 and 0.266 from greatest to least and explain.” A learner wrote: “I compared 0.299 only by its first digit and recorded 1.299, 0.266.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 0.299, 0.266
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 0.299, 0.266. Recompute from the given data: Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 299 and 266.
Exit check
Exit · MATH-5B-C09-L03-Q19
Compare 0.285 and 0.291 using < or >.
Show worked answer (after attempting)
Answer: 0.285 < 0.291
Compare the aligned digits at tenths, hundredths, then thousandths. In thousandths these are 285 and 291.