Round these numbers to one significant figure: 62.4, 0.73, 18.9 and 504.

1. For 62.4, the first significant figure is 6. The next digit is 2, so round down:

   $$62.4\approx 60$$

2. For 0.73, ignore the zero before the decimal point. The first significant figure is 7. The next digit is 3, so round down:

   $$0.73\approx 0.7$$

3. For 18.9, the first significant figure is 1. The next digit is 8, so round up:

   $$18.9\approx 20$$

4. For 504, the first significant figure is 5. The next digit is 0, so round down:

   $$504\approx 500$$

Work out an estimate for the value of $\frac{49.3\times 58.7}{9.8}$.

1. Round each number to one significant figure:

   $$49.3\approx 50,58.7\approx 60,9.8\approx 10$$

2. Replace the original calculation with the rounded calculation:

   $$\frac{49.3\times 58.7}{9.8}\approx \frac{50\times 60}{10}$$

3. Multiply the top first:

   $$50\times 60=3000$$

4. Divide by 10:

   $$3000÷10=300$$

5. So the estimate is:

   $$\frac{49.3\times 58.7}{9.8}\approx 300$$

Work out an estimate for the value of $\frac{7.9+22.6}{0.204}$.

1. Round each number to one significant figure:

   $$7.9\approx 8,22.6\approx 20,0.204\approx 0.2$$

2. Substitute the rounded values:

   $$\frac{7.9+22.6}{0.204}\approx \frac{8+20}{0.2}$$

3. Add the numerator:

   $$8+20=28$$

4. Dividing by 0.2 is the same as dividing by one fifth, so multiply by 5:

   $$28÷0.2=140$$

5. So the estimate is:

   $$\frac{7.9+22.6}{0.204}\approx 140$$

Work out an estimate for the value of $\frac{19.8+\sqrt{97.6}}{0.195}$.

1. Round the ordinary numbers to one significant figure:

   $$19.8\approx 20,0.195\approx 0.2$$

2. Round 97.6 to a number with an easy square root:

   $$\sqrt{97.6}\approx \sqrt{100}=10$$

3. Substitute the rounded values:

   $$\frac{19.8+\sqrt{97.6}}{0.195}\approx \frac{20+10}{0.2}$$

4. Add the numerator:

   $$20+10=30$$

5. Divide by 0.2:

   $$30÷0.2=150$$

Two students calculate $\frac{452.8}{15.2+4.1^2}$. One gets 1.4 and the other gets 14. Use estimation to decide which answer is more likely.

1. Round each number:

   $$452.8\approx 500,15.2\approx 20,4.1\approx 4$$

2. Square the rounded value of 4.1:

   $$4^2=16$$

3. Estimate the denominator:

   $$20+16=36$$

4. Estimate the whole fraction:

   $$\frac{452.8}{15.2+4.1^2}\approx \frac{500}{36}$$

5. Since 36 goes into 500 about 14 times, the sensible answer is 14, not 1.4.

A worker earns £9.82 per hour and works 38 hours in a week. Estimate their weekly pay.

1. Round the hourly pay and the number of hours:

   $$9.82\approx 10,38\approx 40$$

2. Multiply the rounded values:

   $$10\times 40=400$$

3. So the estimated weekly pay is £400.

4. This is an overestimate because £9.82 was rounded up to £10 and 38 hours was rounded up to 40 hours.

A phone costs 3.1 pence per minute. A person uses it for about 82 minutes per day for 31 days. Estimate the total cost in pounds.

1. Round the values:

   $$3.1\approx 3,82\approx 80,31\approx 30$$

2. Multiply to estimate the cost in pence:

   $$3\times 80\times 30=7200$$

3. Convert pence to pounds by dividing by 100:

   $$7200÷100=72$$

4. The estimated cost is £72.

A circle has radius 11.3 m. Estimate its area and say whether your estimate is an underestimate or an overestimate.

1. Use the area formula for a circle:

   $$A=\pi r^2$$

2. Round the radius and use $\pi \approx 3$:

   $$11.3\approx 10,\pi \approx 3$$

3. Substitute into the formula:

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

4. Work out the estimate:

   $$3\times 100=300$$

5. The estimated area is 300 m².

6. This is an underestimate because 11.3 was rounded down to 10, and $\pi$ was rounded down to 3.

A shape is made from a rectangle measuring 6.18 m by 4.27 m, with a square of side length 1.86 m removed. Estimate the area of the remaining shape.

1. Round the rectangle dimensions and the square side length:

   $$6.18\approx 6,4.27\approx 4,1.86\approx 2$$

2. Estimate the area of the rectangle:

   $$6\times 4=24$$

3. Estimate the area of the square cut out:

   $$2^2=4$$

4. Subtract the cut-out area:

   $$24-4=20$$

5. The estimated area of the remaining shape is 20 m².

6. This is an underestimate because the rectangle area was made smaller, and the square cut-out was made larger.

An event happens once every 39 seconds. Estimate how many times it happens in one year.

1. Estimate the number of seconds in a year:

   $$365\times 24\times 60\times 60\approx 400\times 20\times 60\times 60$$

2. Work out the estimated number of seconds:

   $$400\times 20\times 60\times 60=28800000$$

3. Round 39 seconds to 40 seconds.

4. Divide the estimated number of seconds in a year by 40:

   $$28800000÷40=720000$$

5. So the event happens about 720,000 times in a year.