ACT Preparation / Unit 7 ACT 0625 worked example, 60 to 90 seconds
Comparing Numbers Written Different Ways
The idea
To compare or order numbers written as fractions, decimals, percents and scientific notation, work in three steps. First, choose one form, usually the decimal. Second, convert every number to it: divide fractions, divide percents by 100, and multiply out scientific notation. Third, line the decimals up by place value and compare digit by digit from the left.
In practice
Worked example: order 3/8, 0.36, 37% and 3.5 × 10⁻¹ from least to greatest. As decimals: 3/8 = 0.375; 0.36; 37% = 0.37; 3.5 × 10⁻¹ = 0.35. In order: 0.35, 0.36, 0.37, 0.375, so 3.5 × 10⁻¹, then 0.36, then 37%, then 3/8.
Where people slip
Write enough decimal places to separate the numbers. Rounded to one place, all four look like 0.4, and the order disappears.
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