Round 47.6, 0.52, 12.4 and 0.184 to 1 significant figure.

1. For 47.6, the first significant digit is 4 and the next digit is 7, so it rounds up to 50.

2. For 0.52, ignore the zero before the decimal point. The first significant digit is 5, so it becomes 0.5.

3. For 12.4, the first significant digit is 1 and the next digit is 2, so it becomes 10.

4. For 0.184, the first significant digit is 1 and the next digit is 8, so it rounds up to 0.2.

Estimate the value of $\frac{47.8\times 61.6}{12.1}$.

1. Round each number to 1 significant figure: 47.8 becomes 50, 61.6 becomes 60, and 12.1 becomes 10.

2. Replace the original calculation with the rounded calculation:

   $$\frac{50\times 60}{10}$$

3. Multiply the numbers on the top:

   $$50\times 60=3000$$

4. Divide by the number on the bottom:

   $$3000÷10=300$$

Estimate the value of $\frac{18.7+62.4}{0.19}$.

1. Round the numbers: 18.7 becomes 20, 62.4 becomes 60, and 0.19 becomes 0.2.

2. Add the rounded numbers on the top:

   $$20+60=80$$

3. Divide by 0.2. Dividing by 0.2 is the same as multiplying by 5:

   $$80÷0.2=400$$

Estimate the value of $\frac{22.4+\sqrt{101.2}}{0.48}$.

1. Round 22.4 to 20, 101.2 to 100, and 0.48 to 0.5.

2. Use the easy square root:

   $$\sqrt{100}=10$$

3. Substitute the rounded values:

   $$\frac{20+10}{0.5}$$

4. Add the top, then divide by 0.5:

   $$30÷0.5=60$$

A calculation is $\frac{426.5}{14.8+3.9^2}$. One calculator answer is 1.4 and another is 14. Use an estimate to decide which is sensible.

1. Round 426.5 to 400, 14.8 to 10, and 3.9 to 4.

2. Estimate the power:

   $$4^2=16$$

3. Estimate the denominator:

   $$10+16=26$$

4. Use 26 as about 30, then estimate:

   $$\frac{400}{30}\approx 13$$

5. The sensible calculator answer is 14, because it is close to 13.

Maya is paid £8.32 per hour and works 41 hours in a week. Estimate her weekly pay and say whether it is an underestimate or an overestimate.

1. Round £8.32 to £8 and 41 hours to 40 hours.

2. Multiply the rounded values:

   $$8\times 40=320$$

3. The estimate is £320.

4. £8.32 was rounded down and 41 was rounded down, so the estimate is an underestimate.

A machine records one event every 58 seconds. Estimate how many events happen in one year.

1. Use easy estimates: 1 year is about 400 days, 1 day is about 20 hours, and 58 seconds is about 60 seconds.

2. Estimate the number of seconds in a year, then divide by 60 seconds per event:

   $$\frac{400\times 20\times 60\times 60}{60}$$

3. Cancel one factor of 60:

   $$400\times 20\times 60$$

4. Calculate the estimate:

   $$400\times 20\times 60=480000$$

A circular flower bed has radius 11.6 m. Estimate its area and say whether the estimate is too small or too large.

1. Round the radius 11.6 m to 10 m, and use $\pi \approx 3$.

2. Substitute into the area formula:

   $$A\approx 3\times 10^2$$

3. Work out the square and multiply:

   $$3\times 100=300$$

4. The estimate is 300 m². Since the radius and $\pi$ were both rounded down, this is an underestimate.

A shape is made from a rectangle measuring 5.26 m by 3.18 m, with a square of side 1.94 m removed. Estimate the remaining area.

1. Round the rectangle to 5 m by 3 m, and the square side to 2 m.

2. Estimate the large rectangle area:

   $$5\times 3=15$$

3. Estimate the square cut-out area:

   $$2^2=4$$

4. Subtract the cut-out area:

   $$15-4=11$$

5. The estimate is 11 m². The rectangle area was rounded down and the cut-out area was rounded up, so the remaining area is an underestimate.