Converting Fractions to Decimals

Worked example

1. 1

   $\frac{7}{10}=0.7$ — Over 10 means tenths. Tenths are the first place after the point, so the 7 goes there.

2. 2

   $\frac{29}{100}=0.29$ — Over 100 means hundredths. That needs two digits after the point, and 29 fills both.

3. 3

   $\frac{3}{100}=0.03$ — Still hundredths, so two digits. 3 is only one digit, so a zero holds the tenths place.

Worked example

1. 1

   $\frac{9}{20}=\frac{9\times 5}{20\times 5}$ — 20 × 5 = 100, so multiply by 5. Do it to the top too, so the fraction keeps its value.

2. 2

   $=\frac{45}{100}$ — 9 × 5 = 45 on top. The bottom is now 100.

3. 3

   $=0.45$ — Over 100 means hundredths: read off two digits after the point.

Worked example

1. 1

   $\frac{4}{5}=\frac{4\times 2}{5\times 2}$ — 5 × 2 = 10, so multiply the top and the bottom by 2.

2. 2

   $=\frac{8}{10}$ — 4 × 2 = 8 on top. The bottom is now 10.

3. 3

   $=0.8$ — Over 10 means tenths: one digit after the point.

Worked example

1. 1

   $\frac{5}{8}=5÷8$ — The fraction line means divide the top by the bottom.

2. 2

   $5.000÷8$ — Write 5 as 5.000. The zeros do not change its value, but they give you digits to divide into.

3. 3

   $5÷8=0\text{r}5$ — 8 does not go into 5, so the answer starts 0. and the 5 is carried.

4. 4

   $50÷8=6\text{r}2$ — 8 × 6 = 48, so 6 with 2 left. 6 is the first digit after the point.

5. 5

   $20÷8=2\text{r}4$ — Carry the 2 onto the next 0 to make 20. 8 × 2 = 16, so 2 with 4 left.

6. 6

   $40÷8=5\text{r}0$ — Carry the 4 to make 40. 8 × 5 = 40 exactly. Nothing is left, so stop.

7. 7

   $\frac{5}{8}=0.625$ — Read the digits in order after the point.

Worked example

1. 1

   $2\frac{3}{5}=2+\frac{3}{5}$ — A mixed number is a whole number plus a fraction. Change the fraction on its own.

2. 2

   $\frac{3}{5}=\frac{6}{10}$ — Multiply the top and the bottom by 2, because 5 × 2 = 10 and tenths are easy to read.

3. 3

   $\frac{6}{10}=0.6$ — Over 10 means one digit after the point.

4. 4

   $2+0.6=2.6$ — Put the whole number back in front of the point.

Worked example

1. 1

   $\frac{11}{4}=11÷4$ — The top is bigger than the bottom, so the answer will be bigger than 1.

2. 2

   $11÷4=2\text{r}3$ — 4 goes into 11 2 whole times with 3 left, so $\frac{11}{4}=2\frac{3}{4}$.

3. 3

   $\frac{3}{4}=0.75$ — A fraction you know by heart from the first card.

4. 4

   $\frac{11}{4}=2.75$ — The 2 goes in front of the point and 0.75 after it.

Worked example

1. 1

   $\frac{5}{6}:6=2\times 3$ — The bottom has a 3, so $\frac{5}{6}$ goes on for ever.

2. 2

   $\frac{4}{9}:9=3\times 3$ — Only 3s. This one goes on for ever too.

3. 3

   $\frac{7}{12}:12=2\times 2\times 3$ — The 2s are fine, but the 3 makes it go on for ever.

4. 4

   $\frac{9}{15}=\frac{3}{5}$ — 15 has a 3, but simplify first: divide the top and the bottom by 3. The 3 cancels.

5. 5

   $\frac{3}{5}=0.6$ — The bottom is now only a 5, so the decimal stops. $\frac{9}{15}$ is the answer.

Worked example

1. 1

   $2÷3=0\text{r}2$ — 3 does not go into 2, so the answer starts 0. and the 2 is carried.

2. 2

   $20÷3=6\text{r}2$ — 3 × 6 = 18, so 6 with 2 left.

3. 3

   $20÷3=6\text{r}2$ — Carry the 2 again: the same 20, the same 6. It will repeat for ever.

4. 4

   $\frac{2}{3}=0.666\dots$ — A recurring decimal. If the question asks you to round, write 0.667 (3 decimal places).

Worked example

1. 1

   $\frac{11}{20}+0.68$ — The question. You cannot add a fraction and a decimal as they are, so make both decimals.

2. 2

   $\frac{11}{20}=\frac{11\times 5}{20\times 5}$ — Multiply the top and the bottom by 5, because 20 × 5 = 100.

3. 3

   $=\frac{55}{100}=0.55$ — 55 hundredths is 0.55: two digits after the point.

4. 4

   $0.55+0.68=1.23$ — Now both are decimals, so add them. Line up the points.

Worked example

1. 1

   $\text{halfway between }\frac{3}{25}\text{ and }0.48$ — The question. Halfway means the middle of the two numbers.

2. 2

   $\frac{3}{25}=\frac{3\times 4}{25\times 4}$ — Multiply the top and the bottom by 4, because 25 × 4 = 100.

3. 3

   $=\frac{12}{100}=0.12$ — 12 hundredths is 0.12.

4. 4

   $0.12+0.48=0.6$ — Add the two numbers.

5. 5

   $0.6÷2=0.3$ — Halve the total to land exactly in the middle.

6. 6

   $0.3-0.12=0.18,0.48-0.3=0.18$ — Check: the gap on each side is the same, so 0.3 really is halfway.

Worked example

1. 1

   $\text{difference between }\frac{17}{20}\text{ and }0.59$ — The question. Difference means the bigger number minus the smaller one.

2. 2

   $\frac{17}{20}=\frac{85}{100}=0.85$ — Multiply the top and the bottom by 5, because 20 × 5 = 100.

3. 3

   $0.85-0.59=0.26$ — 0.85 is bigger than 0.59, so take 0.59 away from it.