L5 · Terminating decimals and fractions

Learning goal

“I can convert a fraction to a terminating decimal and a terminating decimal back to a fraction in lowest terms - and I can predict from the denominator whether a fraction's decimal will terminate.”

Terminating decimal — a decimal that ends: 0.75 and 0.375 terminate; they do not go on forever.

Numerator — the number above the line in a fraction: in 3/4 it is 3 (counts the parts taken).

Denominator — the number below the line: in 3/4 it is 4 (names the size of the parts).

Lowest terms — a fraction whose numerator and denominator share no factor except 1: 9/20 is in lowest terms; 45/100 is not.

Worked example

Write 3/4 as a decimal - two ways. Step 1 (equivalent-fraction way): quarters can become hundredths. 4 x 25 = 100, so 3/4 = 75/100 = 0.75. Step 2 (division way): a fraction IS a division: 3 / 4. 4 goes into 3.00 exactly 0.75 times - the division finishes, with nothing left over. Step 3: On the equivalence bar, 3 of 4 equal parts and 75 of 100 equal parts shade the same length; on the number line both land on the same point, 0.75. Say it plainly: a decimal is just a fraction whose denominator is a power of 10. If you can scale the denominator to 10, 100 or 1,000, the decimal terminates.

Check yourself — explain it

3/4 = 0.75 works because...

Paired problem — example still visible

Write 2/5 as a decimal. -> 2/5 = 4/10 = 0.4

Faded completion — last step is yours

"7/20: 20 x 5 = 100, so 7/20 = ___/100 = ___" -> 35; 0.35

Ready to practise?

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

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