Did you know? The fraction 3/8, the decimal 0.375 and the percentage 37.5% are three different ways to say exactly the same amount. When a Secondary 4 G1 student can move between them confidently, questions about probability, finance and data become much easier to read.
Quick answer for Bukit Timah families: a fraction describes a part compared with a whole, a decimal uses place value, and a percentage compares with 100. For SEC G1 Mathematics, convert using division, multiplication by 100 and equivalent fractions—but always decide what the quantity represents before choosing a method.
One value, three mathematical languages
Suppose three out of eight equally sized pieces are shaded. As a fraction, that is 3/8. Divide 3 by 8 and you obtain 0.375. Multiply the decimal by 100 to express it as 37.5%. The quantity did not change; only its representation changed.
A tutor can ask the learner to explain each form: three of eight parts; 375 thousandths of a whole; or 37.5 out of every hundred in proportional terms. That explanation helps prevent the habit of moving a decimal point without understanding why.
Example 1: fraction to decimal to percentage
Convert 7/20. The decimal is 7 ÷ 20 = 0.35. Then 0.35 × 100 = 35%. A quick independent check is to rewrite 7/20 as 35/100 by multiplying numerator and denominator by five.
Try 3/4 next. It equals 0.75 and therefore 75%. If a student reports 0.75%, they have confused the decimal with its percentage representation. In percentage form, the numeral must be multiplied by 100 and accompanied by the percent symbol.
Example 2: decimal to a simplified fraction
Write 0.125 as a fraction. It means 125 thousandths, so start with 125/1000. Divide numerator and denominator by 125: 1/8. As a percentage, 0.125 × 100 = 12.5%.
Now try 0.06. It means 6/100, simplifying to 3/50, and equals 6%. The number of decimal places helps create the denominator; simplifying the fraction is a separate step.
Example 3: percentage back to a fraction
Convert 4.5% to a fraction. Divide by 100: 4.5/100 = 0.045. Express this as 45/1000 and simplify by five to obtain 9/200.
The percent symbol literally means ‘per hundred’. When the percentage includes a decimal, first turn it into an ordinary fraction over 100, then clear the decimal if necessary. This method is more reliable than guessing a denominator.
Example 4: compare different representations
Which is larger: 3/8 or 40%? Since 3/8 = 37.5%, the larger value is 40%. Equivalently, 40% = 0.40 while 3/8 = 0.375. Comparing like with like avoids a misleading judgement based on the displayed digits.
A negative example follows the same rules: −3/4 = −0.75 = −75%. On a number line, −75% is smaller than −50%, even though 75 is the larger positive digit. The sign and the chosen unit matter.
What about a percentage greater than 100%?
The number 125% represents 125/100 = 1.25 = 5/4. It is greater than the reference whole. Percentages used to compare quantities can exceed 100%, although a probability cannot exceed 100%.
For example, 125% of 80 is 1.25 × 80 = 100. That question is about a quantity relative to a starting amount, not about the probability of an event. Reading the context helps identify which interpretation is possible.
A four-part conversion checklist
- Fraction to decimal: divide the numerator by the denominator.
- Decimal to percentage: multiply by 100 and write the percent symbol.
- Percentage to decimal: divide by 100 and remove the percent symbol.
- Decimal to fraction: use the place-value denominator and simplify.
Keep a sense of size. A positive fraction smaller than one should give a decimal below one and a percentage below 100%. If the answer changes from 3/8 to 375%, something went wrong.
How does this support the official G1 syllabus?
The SEAB 2027 G1 Mathematics K110 syllabus includes operations on fractions and decimals in N1, percentages as fractions or decimals in N3, and ratio comparisons in N2. These number skills connect to both exam papers and to real-world questions about quantities and data.
For the 2027 K110 examination, Paper 1 and Paper 2 each last 90 minutes and each contain Number and Algebra. Students sitting their examinations in 2026 should follow their actual registered 2026 syllabus rather than automatically treating the 2027 K110 format as their own.
Five-minute home practice
Ask: 1/5 equals what decimal and percentage? Answer: 0.2 and 20%. Next: 0.48 equals what simplified fraction? Answer: 48/100 = 12/25. Finally: 2.5% equals what decimal? Answer: 0.025.
Ask the learner to solve one question again in the reverse direction without notes. If the conversion works only when the question starts as a fraction, give a varied sequence of representations instead of repeating identical drills.
How small-group tuition can diagnose the problem
If a student makes a conversion error, a tutor should check whether they misunderstand place value, simplify fractions incorrectly or forget the change between decimal and percentage notation. The unchanged eduKateSG Clementi small-group Mathematics reference describes a three-pupil teaching model for Secondary 1; check directly for current Secondary 4 G1 services, venues and vacancies rather than assuming them from that page.
Frequently asked questions
Is 0.5 the same as 0.5%? No. 0.5 is 50%, while 0.5% is 0.005.
Can a percentage exceed 100%? Yes, when it describes a quantity larger than its reference amount.
Can a probability exceed 100%? No. Ordinary probabilities lie between 0% and 100%.
Continue with these G1 Mathematics guides
Read fractional and decimal ratios, reverse percentages, and single-event probability.