Decimals and fractions (age 10+)
Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts
What a learner can do afterwards
- Convert between fractions and decimals using division, place value or equivalent fractions, and convert between decimals and percentages (for example, 3/8 = 0.375)
- State that 1/5 = 0.2 = 20% from memory
- Use equivalences between fractions, decimals and percentages to compare 30%, 1/3, and 0.35 and put them in order
1 · Read
You have used fractions to show division. Divide the top number by the bottom number: 3/8 means 3 ÷ 8. The decimal shows the same amount. Fractions can exceed one whole: 7 ÷ 2 gives 3 remainder 1. The remainder contributes 1/2 = 0.5, so 7/2 = 3.5. Compare whole-number parts first. After the decimal point, the first place is tenths, the second is hundredths and the third is thousandths.
Write 3 as 3.000. Since 3 is less than 8, start with 0 and a decimal point. Divide 30 tenths by 8: 3 tenths, remainder 6 tenths. Regroup as 60 hundredths: 7 hundredths, remainder 4 hundredths. Regroup as 40 thousandths: 5 thousandths, no remainder. So 3 ÷ 8 = 0.375 exactly. Rounding gives an estimate if it changes the value. Rounding to three decimal places leaves 0.375 unchanged.
Percent means out of 100. Divide a percentage number by 100 to write it as a decimal: 18% = 18/100 = 0.18. To write a decimal as a percentage, multiply by 100 and add %. For example, 0.375 = 37.5%. Remember the common equivalence 1/5 = 0.2 = 20%.
One fifth is also 0.2 of the whole, or 20%.
Compare fractions, decimals and percentages by writing them as decimals. For 30%, 1/3 and 0.35, compare 0.30, 0.333... and 0.35. The dots mean the 3s keep repeating. Compare digits from left to right. Their hundredths digits are 0, 3 and 5, so 30% < 1/3 < 0.35. Writing 1/3 as 0.333 gives an estimate that leaves out the continuing 3s.
The bars use the same whole. The bar for 1/3 shows an approximate value.
To write a decimal as a fraction, read its place value. For example, 0.9 is nine tenths, or 9/10. A decimal with two places can be written over 100: 0.12 = 12/100. For simplest form, divide the top and bottom by the same common factor. Here, divide both by 4 to get 3/25. Stop when no whole-number factor greater than 1 divides both.
Nine shaded tenths show both 0.9 and 9/10.
You can also make an equivalent fraction with a denominator of 10 or 100. Multiply the top and bottom by the same number to keep the value equal. For 9/25, multiply both by 4: 9/25 = 36/100 = 0.36.
A fraction is a division: work it out, and you get the matching decimal and percent.
Seven questions and two readings were written for this dataset. The seven-tenths question was adapted from Carl Yao's Portland Community College problem. The retained comparison and conversion questions were adapted from Open Middle material credited to Owen Kaplinsky and Robert Kaplinsky. Two readings were adapted from Khan Academy material, and four linked videos are credited to Khan Academy in the source records. Terms for retained third-party material have not been verified.
2 · Watch
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Where it sits
Where this leads
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