What you'll learn
- How fractions, decimals and percentages all describe part of a whole.
- How to convert between the three forms.
- How to compare and order a mixture of forms.
- How to show enough working for 1-mark and 2-mark questions.
The big idea: parts of a whole
Fractions, decimals and percentages are three different ways to describe the same kind of thing: part of a whole. The whole means the full amount, such as one complete shape, one full salary, or 100%.
Key words
- A fraction has a top number, called the numerator, and a bottom number, called the denominator. It shows equal parts of a whole.
- A decimal uses a decimal point. Place value means the position of each digit tells you its value, such as tenths, hundredths and thousandths.
- A percentage means “out of 100”.
- To simplify a fraction means to divide the numerator and denominator by the same number, making the fraction look simpler without changing its value.
Writing a percentage as a fraction
- Start with 14%.
-
Percent means out of 100, so write it as a fraction:
14%=1410014\% = \frac{14}{100}14%=10014 -
Simplify by dividing the numerator and denominator by 2:
14100=750\frac{14}{100} = \frac{7}{50}10014=507
Decimals to percentages
To change a decimal to a percentage, multiply by 100. This moves the decimal point two places to the right.
Changing 0.37 to a percentage
- Start with the decimal 0.37.
-
Multiply by 100:
0.37×100=370.37 \times 100 = 370.37×100=37 -
Add the percentage sign: 37%.
One decimal place
0.3 is 30%, not 3%, because multiplying by 100 moves the decimal point two places to the right.
Percentages to decimals
To change a percentage to a decimal, divide by 100. This moves the decimal point two places to the left.
Changing 7% to a decimal
- Start with 7%.
-
Divide by 100:
7÷100=0.077 \div 100 = 0.077÷100=0.07 -
So 7% as a decimal is 0.07.
Two quick moves
Decimal to percentage: move right two places. Percentage to decimal: move left two places.
Decimals to fractions
Use the number of digits after the decimal point.
- 1 digit after the point means tenths.
- 2 digits after the point means hundredths.
- 3 digits after the point means thousandths.
Writing 0.025 as a fraction
-
There are 3 digits after the decimal point, so use thousandths.
-
Write 0.025 as 25 thousandths:
0.025=2510000.025 = \frac{25}{1000}0.025=100025 -
Simplify by dividing the numerator and denominator by 25:
251000=140\frac{25}{1000} = \frac{1}{40}100025=401
Fractions to decimals
A fraction bar means “divide”. For many Grade 2 questions, it is quicker to make the denominator 10 or 100 if you can.
Equivalent fractions
Equivalent fractions have the same value, even though the numerator and denominator look different.
Changing a fraction to a decimal
- Start with 45\frac{4}{5}54.
-
Make the denominator 10 by multiplying the numerator and denominator by 2:
45=810\frac{4}{5} = \frac{8}{10}54=108 -
Eight tenths is 0.8, so 45\frac{4}{5}54 as a decimal is 0.8.
Fractions to percentages
Because a percentage means “out of 100”, try to make the denominator 100.
Changing a fraction to a percentage
-
Start with 1120\frac{11}{20}2011.
-
Change the denominator from 20 to 100 by multiplying by 5. Do the same to the numerator:
1120=55100\frac{11}{20} = \frac{55}{100}2011=10055 -
Since 55100\frac{55}{100}10055 means 55 out of 100, the answer is 55%.
Changing only one part
If you multiply the denominator by 5, you must multiply the numerator by 5 as well. Otherwise you have changed the value of the fraction.
Comparing two amounts
When deciding which is bigger, convert both numbers to the same form first. Decimals are often easiest.
Checking a claim
-
A claim says 16% is greater than 0.2. Convert 16% to a decimal:
16÷100=0.1616 \div 100 = 0.1616÷100=0.16 -
Compare 0.16 with 0.2. Because 0.16<0.200.16 < 0.200.16<0.20, 16% is smaller.
-
The claim is not correct.
Ordering mixed forms
For ordering questions, convert everything to one form, put the converted numbers in order, then write the original numbers in that order.
Ordering a mixed list
- Start with the list: 42%, 12\frac{1}{2}21, 0.47, 25\frac{2}{5}52, 0.405.
-
Convert the percentages and fractions to decimals:
42%=0.4212=0.525=0.4\begin{aligned} 42\% &= 0.42 \\ \frac{1}{2} &= 0.5 \\ \frac{2}{5} &= 0.4 \end{aligned}42%2152=0.42=0.5=0.4 -
Compare using the same number of decimal places:
0.400<0.405<0.420<0.470<0.5000.400 < 0.405 < 0.420 < 0.470 < 0.5000.400<0.405<0.420<0.470<0.500 -
Write the original values in order: 25\frac{2}{5}52, 0.405, 42%, 0.47, 12\frac{1}{2}21.
Comparing before converting
0.9 may look smaller than 75% because it starts with 0, but 0.9 is 90%, so it is larger.
Worded comparisons: save or spend
If someone spends some money and saves “the rest”, remember that the whole amount is 100% or one whole.
Comparing savings
- Maya saves 38%. Leo spends 35\frac{3}{5}53 and saves the rest. Since the whole is 55\frac{5}{5}55, Leo saves:
$$
\frac{5}{5} - \frac{3}{5} = \frac{2}{5}
$$
2. Convert 25\frac{2}{5}52 to a percentage:
$$
\frac{2}{5} = \frac{40}{100} = 40\%
$$
3. Compare 38% and 40%. Leo saves more.
In the exam
- Convert everything to one form before comparing; decimals are usually quickest.
- Show one clear line of working for 2-mark questions, especially when finding “the rest”.
- Check place value carefully: 4% is 0.04, not 0.4.
Check yourself
- Can you explain why 0.08 is the same as 8%?
- Can you turn 34\frac{3}{4}43 into a percentage?
- If one number is a decimal and one is a percentage, what should you do before deciding which is bigger?
