Fractions, Decimals & Percentages Flashcards

All 16 cards in this deck

How do you convert a fraction to a decimal?

e.g. $\frac{3}{8}$

Divide the numerator by the denominator.

$3 \div 8 = 0.375$

How do you convert a terminating decimal to a fraction in its simplest form?

e.g. $0.36$

Write the digits over 10, 100, 1000... (one zero per decimal place), then simplify.

$0.36 = \frac{36}{100} = \frac{9}{25}$

How do you convert a percentage to a fraction in its simplest form?

e.g. $45\%$

Write it over 100, then simplify.

$45\% = \frac{45}{100} = \frac{9}{20}$

How can you tell from its denominator whether a fraction converts to a terminating decimal?

In its simplest form, the denominator has only 2 and/or 5 as prime factors.

e.g. $\frac{7}{40}$ terminates because $40 = 2^3 \times 5$

True or false? $0.5\%$ written as a decimal is $0.5$.

False. $0.5\% = 0.5 \div 100 = 0.005$.

What does the dot notation $0.\dot{1}\dot{7}$ mean?

$0.171717\ldots$ — the block 17 repeats forever.

How do you convert a fraction to a recurring decimal?

e.g. $\frac{5}{11}$

Divide the numerator by the denominator and put dots on the repeating block.

$5 \div 11 = 0.4545\ldots = 0.\dot{4}\dot{5}$

What are the steps to convert a recurring decimal to a fraction algebraically?

e.g. $x = 0.\dot{5}$

1. Multiply $x$ by a power of 10 so the recurring parts line up: $10x = 5.555\ldots$
2. Subtract to get a terminating decimal: $10x - x = 5$, so $9x = 5$
3. Divide and simplify: $x = \frac{5}{9}$

True or false? You can prove a recurring decimal equals a fraction by writing it as a terminating decimal to 5 decimal places and putting it over $100\,000$.

False. That only gives an approximation and scores no accuracy marks; you must use two multiples of $x$ whose subtraction gives a terminating decimal.

How do you put a mixed set of fractions, decimals and percentages in order?

e.g. $\frac{3}{5}$, $55\%$, $0.58$

Convert them all to decimals, compare, then write the answer using the original forms.

$0.6$, $0.55$, $0.58$ → $55\%$, $0.58$, $\frac{3}{5}$

True or false? $0.246$ is greater than $0.6$ because it has more digits.

False. Compare place value from the left: $2$ tenths $<$ $6$ tenths, so $0.246 < 0.6$.

True or false? $-\frac{3}{4} < -\frac{1}{2}$

True. $-0.75$ lies further left on the number line than $-0.5$, so it is smaller.

What does it mean to write a list of numbers in ascending order?

From smallest to largest.

How do you compare two fractions with different denominators without a calculator?

e.g. $\frac{3}{4}$ and $\frac{5}{7}$

Rewrite both with a common denominator (or convert both to decimals) and compare numerators.

$\frac{21}{28} > \frac{20}{28}$, so $\frac{3}{4}$ is larger

What are the steps to convert a recurring decimal with a non-recurring digit at the front into a fraction?

e.g. $x = 0.1\dot{6}$

1. Multiply so the recurring part starts straight after the point: $10x = 1.\dot{6}$
2. Multiply again so the same pattern repeats: $100x = 16.\dot{6}$
3. Subtract and simplify: $90x = 15$, so $x = \frac{15}{90} = \frac{1}{6}$

When a recurring decimal has non-recurring digits at the front, how do you choose the two multiples of $x$ to subtract?

e.g. $x = 0.2\dot{3}\dot{1}$

Choose multiples whose decimal parts are identical, so the subtraction gives a terminating decimal.
e.g. $10x = 2.\dot{3}\dot{1}$ and $1000x = 231.\dot{3}\dot{1}$