L2 · Expressing relative frequency: fraction, decimal, percent

Learning goal

“I can express the same relative frequency three ways - as a fraction, a decimal, and a percent - and convert between them without changing the value: 7/20 = 0.35 = 35%.”

Percent — a number out of 100. 35% means 35 out of 100, written with the % sign.

Convert — to change the form of a number without changing its value, like rewriting 7/20 as 0.35.

Equivalent — equal in value, different in appearance: 7/20, 0.35, and 35% are equivalent.

Hundredth — one hundredth, 1/100 = 0.01. Percents count hundredths: 35% is 35 hundredths.

Worked example

In a target game, an outcome happened 7 times in 20 trials. Its relative frequency is 7/20. Step 1: Rewrite out of 100. 20 x 5 = 100, so multiply both numbers by 5: 7/20 = 35/100. Step 2: As a decimal, 35 hundredths is 0.35 (3 tenths and 5 hundredths on the place-value chart). Step 3: As a percent, 35 out of 100 is 35%. One value, three forms: 7/20 = 0.35 = 35%. On a 100-grid, 35 of the 100 squares are shaded - the same share every time.

Check yourself — explain it

7/20 and 35% are equivalent because...

Paired problem — example still visible

Write 3/5 as a decimal and a percent. -> 3/5 = 6/10 = 0.6 = 60%

Faded completion — last step is yours

"9/25: multiply both numbers by 4 -> ___/100, so 9/25 = ___%." -> 36/100; 36%

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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