Fractions, decimals and percentages

We want to write 3/8 as a decimal and a percentage. We make an equivalent fraction with the denominator 1 000.

1. 8 does not go into 100 exactly, but 8 · 125 = 1 000. We multiply the numerator and denominator by 125. The value does not change.

   $\frac{3}{8}$ = (3 · 125)/(8 · 125) = $\frac{375}{1000}$

2. 375 thousandths is 0.375. A calculator gives the same answer: 3 ÷ 8.

   $\frac{375}{1000} = 0$.375

3. We multiply by 100 to get the percentage.

   0.375 · 100 = 37.5

4. 3/8 is 0.375 or 37.5%.

3/8 is a little under 4/8 = 50%, and 37.5% is a little under 50%. That is reasonable. Check: 0.375 · 8 = 3.

We want to write 45% as a decimal and as a fraction in its simplest form.

1. Percent means hundredths.

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

2. For the decimal, we divide by 100.

   45 ÷ 100 = 0.45

3. Both 45 and 100 can be divided by 5.

   $\frac{45}{100}$ = (45 ÷ 5)/(100 ÷ 5) = $\frac{9}{20}$

4. 9 and 20 have no common factor other than 1, so 9/20 is the simplest form.

9 ÷ 20 = 0.45 = 45%. Both the decimal and the fraction are correct.

We want to write 7/20 as a percentage without a calculator. So we want the denominator to be 100.

1. 20 · 5 = 100, so we multiply the numerator and denominator by 5.

   $\frac{7}{20}$ = (7 · 5)/(20 · 5) = $\frac{35}{100}$

2. 35 hundredths is 35%, or 0.35.

   $\frac{35}{100} = 35$% = 0.35

7 ÷ 20 = 0.35, and 0.35 · 100 = 35. The answer 35% is correct.