Converting Fractions, Decimals and Percentages

Express the fraction as an equivalent number of hundredths.

Find an equivalent fraction with denominator 10, or divide the numerator by the denominator.

A percentage counts hundredths.

A percentage is a number of hundredths.

Read the decimal using place value.

Start with a fraction over 100, then divide top and bottom by the same factor.

1. 35\%=\frac{35}{100}.
2. Divide both numbers by 5: \frac{35}{100}=\frac{7}{20}. The missing numerator is 7.

Make the denominator 100.

1. \frac{1}{4}=\frac{25}{100} because both numbers are multiplied by 25.
2. That is 25\%.

The zero in the tenths column matters: this is eight hundredths.

1. 0.08=\frac{8}{100}.
2. It is 8\%, not 80\%.

Write forty-five hundredths, then cancel a common factor.

1. 0.45=\frac{45}{100}.
2. Dividing top and bottom by 5 gives \frac{9}{20}, which cannot be simplified further.

Divide 3 by 8 to find the decimal value, then convert it to a percentage.

1. \frac{3}{8}=3\div8=0.375.
2. 0.375\times100=37.5, so the percentage is 37.5\%.

Convert all four values to decimals before comparing.

1. \frac{7}{10}=0.70, 68\%=0.68, and \frac{3}{4}=0.75.
2. The decimals are 0.70, 0.68, 0.72 and 0.75.
3. The largest is 0.75, so choose \frac{3}{4}.

Write the score as a fraction, then make its denominator 100.

1. The score is \frac{17}{20}.
2. Multiply top and bottom by 5: \frac{17}{20}=\frac{85}{100}=85\%.

One whole is 100%; this value is more than one whole.

1. Multiply by 100: 1.25\times100=125.
2. So 1.25=125\%. The extra quarter contributes another 25\% above 100\%.

Find how many counters are not red, then express this amount out of 100.

1. The number not red is 50-16=34.
2. The fraction not red is \frac{34}{50}=\frac{68}{100}.
3. So 68\% of the counters are not red.

First convert Jae’s score to a percentage. A percentage-point gap is the difference between the two percentage numbers.

1. Jae’s score is \frac{18}{25}=\frac{72}{100}=72\%.
2. The difference is 72-70=2 percentage points.

Convert both limits to hundredths, then consider fractions with denominator 20.

1. The upper limit is 67\%=0.67.
2. In twentieths, \frac{12}{20}=0.60, \frac{13}{20}=0.65 and \frac{14}{20}=0.70.
3. Only 0.65 is strictly between 0.62 and 0.67. The required fraction is \frac{13}{20}, so its numerator is 13.

Express the green and blue shares in the same form before finding the remainder.

1. The blue share is 0.4\times100=40\%.
2. Green and blue together have 37.5+40=77.5\% of the votes.
3. The rest choose red: 100-77.5=22.5\%.

Put both ends in decimal form. Halve their gap, then add it to the smaller value.

1. \frac{4}{5}=0.8. The gap is 0.8-0.35=0.45.
2. Half the gap is 0.45\div2=0.225.
3. The halfway value is 0.35+0.225=0.575.
4. As a percentage, 0.575\times100=57.5, so the answer is 57.5\%.

Convert all three amounts to percentages. Compare the percentage numbers, then subtract the largest and smallest.

Part (a)

1. \frac{11}{8}=1.375=137.5\%. B gives 135\% and C gives 137\%.
2. 137.5 is the largest percentage, so A gives the greatest amount.

Part (b)

1. The largest percentage is 137.5\% and the smallest is 135\%.
2. The gap is 137.5-135=2.5 percentage points.

\frac{1}{3} has a repeating decimal. Compare each option with several decimal places of it.

1. \frac{1}{3}=0.333333\ldots. Convert the options: 33\%=0.33, and \frac{8}{25}=0.32.
2. The gaps from one third are approximately 0.003333, 0.006667, 0.013333 and 0.000333, in the order shown.
3. The smallest gap belongs to 0.333. This is closest, although it is not exactly equal to one third.