L7 · Ordering fractions, decimals and whole numbers

Learning goal

“I can order any mix of positive fractions, decimals (to thousandths) and whole numbers by choosing a strategy - benchmarks, place value, or converting everything to one form - and I can defend my order.”

Benchmark — a familiar landing point used for comparison: 0, 1/2 and 1 are the benchmarks for numbers between 0 and 1.

Place value — the value of a digit by its position: in 0.405 the 4 is 4 tenths, the 0 is 0 hundredths, the 5 is 5 thousandths.

Thousandths — the third place after the decimal point: 0.001 is one thousandth.

Equivalent form — the same number written differently: 3/5 and 0.6 are equivalent forms of one number.

Worked example

Sort 0.35, 4/9, 0.52 and 5/6 into zones: below 1/2, between 1/2 and 1. Step 1: The benchmark 1/2 = 0.5 splits the line. 0.35 < 0.5: zone 1. 4/9: half of 9 is 4.5, and 4 < 4.5, so 4/9 < 1/2: zone 1. Step 2: 0.52 > 0.5: zone 2. 5/6: half of 6 is 3, and 5 > 3, so 5/6 > 1/2: zone 2. Step 3: Inside zone 1, refine: 4/9 = 0.444..., which is more than 0.35. Zone 1 order: 0.35 < 4/9. Zone 2: 5/6 is about 0.833 > 0.52. Say it plainly: benchmarks do the rough sorting for free. Only numbers in the same zone need exact comparison work.

Check yourself — explain it

4/9 is less than 1/2 because...

Paired problem — example still visible

Which zone does 7/12 live in, and why? -> Between 1/2 and 1 - half of 12 is 6, and 7 > 6.

Faded completion — last step is yours

"0.48, 3/7, 0.61: zones are below-1/2, below-1/2 (3/7: half of 7 is 3.5, 3 < 3.5), above-1/2. So the largest is ___" -> 0.61

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