L4 · Fractions and decimals: denominators of 10 and 100 only

Learning goal

“I can switch between a fraction with denominator 10 or 100 and its decimal - they are the same number, at the same point on the number line.”

Decimal — a number written with a decimal point, like 0.7; it is another way to write a fraction.

Decimal point — the dot that separates the wholes from the parts of a whole.

Tenth — one of 10 equal parts of a whole; 1/10 = 0.1.

Hundredth — one of 100 equal parts of a whole; 1/100 = 0.01.

Worked example

Write 7/10 as a decimal, and 0.4 as a fraction. Step 1: A denominator of 10 means tenths. 7/10 is "seven tenths," written 0.7 - the 7 sits in the tenths place, right after the decimal point. Step 2: Going the other way: 0.4 is "four tenths," written 4/10. Model both ways, side by side: a bar cut into 10 equal parts with 7 shaded (7/10) AND a 0-2 number line marked in tenths where 0.7 and 7/10 are marked at the same point. Say it plainly: the decimal and the fraction are two names for one number. Nothing is "converted into" a different number.

Check yourself — explain it

In 0.7, what does the 7 tell us?

Paired problem — example still visible

Write 3/10 as a decimal, and write 0.9 as a fraction. -> 0.3; 9/10

Faded completion — last step is yours

"0.5 is five tenths, so 0.5 = ___/10, which also simplifies to ___." -> 5/10; 1/2

Ready to practise?

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

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